George Olatokunbo Okikiolu

Born:

place: Nigeria

area of degree:

pre-doctoral education:

doctoral institution:

current (12/98) employment

Dr. George O. Okikiolu is the father of **Katherine
Okikiolu**. The two of them are one of the few successful
father-daughter researchers combinations in mathematics. He has
published more papers, over two hundred, than any other Black
Mathematician. His first paper appeared in 1967, and his Ph.D.
was in 1972.

In the late 1970s, Dr. George Okikiolu formed a company, Okikiolu Scientific and Industrial Organization, London which published his first book and publishes a journal, Bulletin of Mathematics.

Research

To date he has published over 290 papers many, after the first 50, appear in his own journal, the Bulletin of Mathemmatics.

1. **Aspects of the theory of bounded integral operators in
$L\sp{p}$-spaces**. Academic Press, London-New York, 1971. ix+522
pp.

2. **Special integral operators. Vol. I. Weierstrass operators
and related integrals.** Okikiolu Scientific and Industrial
Organization, London, 1980. ix+306 pp. ISBN: 0-905499-04-2

3. **Special integral operators. Vol. II. Poisson operators,
conjugate operators, and related integrals.** Okikiolu Scientific
and Industrial Organization, London, 1981. x+507 pp. ISBN: 0-905499-05-0

Selected papers in other publications

29. *Interpolation theorems for operators relatively bounded
by differential-type transformations,* J. Reine Angew. Math.
**277** (1975), 178--192.

28. *Uniformly bounded projections and semi-groups of operators,*
Proc. Cambridge Philos. Soc. **75** (1974), 199--217.

27. *On Fourier transform multipliers in $L\sp{p}$,* J.
Austral. Math. Soc. **13** (1972), 219--223.

28. *On inequalities for integral operators,* Glasgow
Math. J. **11** (1970), 126--133.

26. *Identities involving conjugate harmonic functions,*
Arch. Math. (Basel) **22** (1971), 505--513.

25. *On the theory and applications of Dirichlet projections,*
J. Reine Angew. Math. **245** 1970 149--164.

24. *Applications of fundamental operators: The operator
$F\sb{\sigma }{}\sp{(\nu )}$,* Proc. London Math. Soc. (3)
**19** 1969 601--624.

23. *On the operator $F\sb{\sigma }{}\sp{(v)}$ and fractional
integrals,* J. London Math. Soc. (2) **1** 1969 619--629.

22. *On semi-groups of operators and the resolvents of their
generators,* Proc. Cambridge Philos. Soc. **66** 1969 533--540.

20. *On maximal functions of fractional order,* Studia
Math. **30** 1968 259--271.

19. *Restrictions on the ranges of bounded linear operators
in $L\sp{p}$ spaces,* J. London Math. Soc. **42** 1967 706--711.

18. *On certain bounded linear transformations in $L\sp{p}$,*
Proc. London Math. Soc. (3) **17**1967 700--714.

17. *On operators which approximate to the identity,*
J. London Math. Soc. **42** 1967 477--483.

16. *On the infinitesimal generator of the Poisson operator.
II. The $n$-dimensional case,* Proc. Cambridge Philos. Soc.
**63** 1967 1021--1025.

15. *A convexity theorem for multilinear functionals,*
II. J. Math. Anal. Appl. **16** 1966 396--404.

14. *Fractional integrals of the $H\sb{\alpha }$-type,*
Quart. J. Math. Oxford Ser. (2) **18** 1967 33--42.

13. *A class of integral operators associated with the Hilbert
transform,* Proc. London Math. Soc. (3) **17** 1967 342--354.

12. *On operators which depend on some parameter,* Proc.
Cambridge Philos. Soc. **63** 1967 359--366.

11. *On integral operators associated with Poisson transforms
and the operator $H\sb{\alpha }$,* J. Austral. Math. Soc. **6**
1966 263--272.

10. *A convexity theorem for multilinear functionals,*
J. Math. Anal. Appl. **16** 1966 165--172.

9. *On certain extensions of the Hilbert operator,* Math.
Ann. **169** 1967 315--327.

8. *$n$th order integral operators associated with Hilbert
transforms,* Pacific J. Math. **18** 1966 343--360.

7. *On the infinitesimal generator of the Poisson operator,*
Proc. Cambridge Philos. Soc. **62** 1966 713--718.

6. Correction and addendum: "On integral operators with
kernels involving Bessel functions". Proc. Cambridge Philos.
Soc. **67** 1970 583--586.

6. *On integral operators with kernels involving Bessel functions,*
Proc. Cambridge Philos. Soc. **62** 1966 477--484.

5. *Bounded linear transformations in $L\sp{p}$ space,*
J. London Math. Soc. **41** 1966 407--414.

4. Correction to: "On operators derived from extensions
of the Fourier transform". Math. Z. **112** 1969 74--76.

4. *On operators derived from extensions of the Fourier transform,*
Math Z. **92** 1966 175--186.

3. *Fourier transforms and the operator $H\sb{\alpha }$,*
Proc. Cambridge Philos. Soc. **62** 1966 73--78.

2. *On integral operators associated with the Hilbert transform,*
Math. Z. **90** 1965 54--70.

1. *A generalisation of the Hilbert transform,* J. London
Math. Soc. **40** 1965 27--30.

Selected papers in the Bulletin of Mathematics

*Relations involving elements of a group with power term
iterates in specified subgroups or relative groups, *Bull.
Math. **65**, 1-52 (1997).

*Compositions of elements which determine relative group
components associated with subgroup of a subgroup, *Bull. Math.
**65**, 53-65 (1997).

*Representations of groups and subgroups as unions of sets
comprising power term iterates, *Bull. Math. **67**, 1-48
(1997).

*Parameter-dependent and mixed variable weight functions
for isometry-invariant operators,* Bull. Math. No. **21**
(1986), 54--67.

*$L\sp p$-convergence of parameter-dependent isometries and
ranges of "isometry-invariant" operators,* Bull.
Math. No. **21** (1986), 35--53.

*Representations of pairs of relatively differential operators,*
Bull. Math. No. **20** (1986), 47--61.

*Product identities for kernels and transforms involving
oscillating or projection-type operators,* Bull. Math. No.
**20** (1986), 25--46. (Reviewer: R. Vittal Rao) 47B38

*Multiple parameter forms of Weierstrass-type operators with
kernels involving orthogonally projected variables,* Bull.
Math. No. **20** (1986), 62--83.

*Multiple parameter fractional integral operators defined
in terms of multiple parameter semigroups,* Bull. Math. No.
**19** (1985), 1--27.

*Representations of and estimates for weighted forms of Fourier
transforms.* Bull. Math. No. **21** (1986), 1--34.

*Fractional integral operators with kernels involving homogeneous
functions.* Bull. Math. No. **19** (1985), 28--62.

*$L\sp p$-estimates for multiplier operators associated with
convolutions.* Bull. Math. No. **15** (1984), 45--69.

*Semigroups of functions with generators defined in terms
of multiplier transforms.* Bull. Math. No. **15** (1984),
1--44.

[11] 87d:42032 Okikiolu, G. O. Pointwise estimates for convolutions involving metric functions. Bull. Math. No. 19

(1985), 63--71. 42B99 (47G05)

[12] 87d:42019 Okikiolu, G. O. Weighted estimates for operators defined as Fourier transform multipliers. Bull. Math.

No. 20 (1986), 1--24. 42B10 (47B38)

[13] 87c:47072 Okikiolu, G. O. Operators of Poisson-type and singular integrals with kernels involving inner products.

Bull. Math. No. 17 (1985), 34--79. (Reviewer: P. Szeptycki) 47G05 (42A85)

[14] 87c:47071 Okikiolu, G. O. Operators of Weierstrass-type with kernels involving inner products. Bull. Math. No. 17

(1985), 1--33. (Reviewer: P. Szeptycki) 47G05 (42A85)

[15] 87b:42020 Okikiolu, G. O. Fourier transforms involving functions of inner products. Bull. Math. No. 16 (1985),

22--51. 42B10

[16] 86m:47064 Okikiolu, G. O. Operator multiplier representations of semigroups generated by linear differential operators

in Euclidean spaces. Bull. Math. No. 12 (1984), 55--71. 47D05 (42B15 47B38)

[17] 86m:47063 Okikiolu, G. O. Semigroups of operators generated by products of commutative infinitesimal generators.

Bull. Math. No. 11 (1983), 28--47. 47D05

[18] 86m:47049 Okikiolu, G. O. Vector-valued forms of weak-norm and $L\sp p$-estimates for bilinear transformations

which define operators mapping between pairs of $L\sp p$-spaces. Bull. Math. No. 16 (1985), 52--72. 47B38 (47G05)

[19] 86m:47048 Okikiolu, G. O. Convolutions involving norms of linear sums of vectors. Bull. Math. No. 12 (1984),

32--54. 47B38

[20] 86m:42026 Okikiolu, G. O. $L\sp p$-estimates for integral operators with singular kernels. Bull. Math. No. 18

(1985), 39--74. 42B20 (47G05)

[21] 86m:42019 Okikiolu, G. O. Transforms involving functions of orthogonally projected variables. Bull. Math. No. 18

(1985), 1--38. 42B10

[22] 86h:47064c Okikiolu, G. O. Derivative-type estimates for operators defined in terms of multiplicative semigroups.

Bull. Math. No. 13 (1984), 63--82. (Reviewer: Alberto Guzman) 47D05 (42B15)

[23] 86h:47064b Okikiolu, G. O. $L\sp{p}$-estimates for fractional integrals associated with semigroups of operators.

Bull. Math. No. 13 (1984), 23--62. (Reviewer: Alberto Guzman) 47D05 (42B15)

[24] 86h:47064a Okikiolu, G. O. Semigroups of operators expressible as multipliers of Fourier transform multipliers.

Bull. Math. No. 13 (1984), 1--22. (Reviewer: Alberto Guzman) 47D05 (42B15)

[25] 86g:47041 Okikiolu, G. O. Kernels of isometric and pairs of inverse operators defined in terms of "representation

functions". Bull. Math. No. 14 (1984), 34--67. 47B38 (44A05 44A15)

[26] 86g:47040 Okikiolu, G. O. Representations of functions in terms of integrals involving exponential kernels. Bull.

Math. No. 14 (1984), 1--33. 47B38 (44A05 44A15)

[27] 86d:26013 Okikiolu, G. O. $L\sp{p}$-estimates for fractional integrals---new proofs of the Hardy\mhy

Littlewood\mhy Sobolev theorems. Bull. Math. No. 12 (1984), 1--31. 26A33 (26D10 42B25)

[28] 85i:47032 Okikiolu, G. O. Weak-norm and $L\sp{p}$-estimates for bilinear expressions which define operators

mapping between pairs of $L\sp{p}$-spaces. Bull. Math. No. 11 (1983), 48--74. 47B38 (42B99 47D99)

[29] 85f:47043 Okikiolu, G. O. Parameter integral representations of semigroups of operators generated by powers of an

infinitesimal generator. Bull. Math. No. 10 (1983), 1--42. (Reviewer: A. B. Buche) 47D05

[30] 85e:44003 Okikiolu, G. O. Operators expressible as Hilbert transform multipliers. Bull. Math. No. 10 (1983),

43--72. 44A15 (47B38)

[31] 85d:42017 Okikiolu, G. O. Estimates for Fourier transforms in terms of derivatives: Fourier transforms in $L\sp{1}$.

Bull. Math. No. 11 (1983), 1--27. (Reviewer: Khélifa Trimèche) 42B10

[32] 84m:47053b Okikiolu, G. O. Semigroups of operators whose generators are defined in terms of differential and

multiplier operators. Bull. Math. No. 9 (1983), 53--74. (Reviewer: A. B. Buche) 47D05 (47E05)

[33] 84m:47053a Okikiolu, G. O. Representations of linear differential operators with domains comprising measurable

functions. Bull. Math. No. 9 (1983), 28--52. (Reviewer: A. B. Buche) 47D05 (47E05 47F05)

[34] 84m:47013 Okikiolu, G. O. Weak-norm and $L\sp{p}$ estimates for weighted forms of bounded operators mapping

between pairs of $L\sp{p}$ spaces. Bull. Math. No. 8 (1983), 49--72. (Reviewer: John Fournier) 47A30 (47B38)

[36] 84m:26020b Okikiolu, G. O. Integrals involving norms of linear sums of vectors, and products of norms of

orthogonal classes. II. Identities and estimates involving minimum value expressio. Bull. Math. 1982, no. 7, 41--63. (Reviewer: A.

B. Buche) 26B15 (26D15)

[37] 84m:26020a Okikiolu, G. O. Integrals involving norms of linear sums of vectors, and products of norms of orthogonal

classes. Bull. Math. 1981/82, no. 6, 30--52. (Reviewer: A. B. Buche) 26B15 (26D15)

[38] 84j:46048b Okikiolu, G. O. Minimum value estimates for bounded linear operators in inner product and $L\sp{p}$

spaces. Bull. Math. 1982, no. 7, 14--40. (Reviewer: Gunnar Sparr) 46E30 (47B38)

[39] 84j:46048a Okikiolu, G. O. Inner products and related norms in $L\sp{p}$-spaces and estimates for bounded linear

operators. Bull. Math. 1982, no. 7, 1--13. (Reviewer: Gunnar Sparr) 46E30 (47B38)

[40] 84j:42030 Okikiolu, G. O. "Conjugately weighted" maximal operators involving parameter-dependent functions.

Bull. Math. 1981/82, no. 3, 2--30. 42B25 (46E35 47B38)

[41] 84i:44004 Okikiolu, G. O. Amendments to: "Weighted inequalities for convolutions: conjugate space estimates" [Bull.

Math. {1981/82}, no. 2, 62--108; MR 83h:44014]. Bull. Math. No. 10 (1983), 73--74. 44A35

[42] 84i:42031 Okikiolu, G. O. Weighted inequalities for positive and maximal operators. Bull. Math. 1981/82, no. 3,

31--83. 42B25 (46E30 47B38)

[43] 84h:47051 Okikiolu, G. O. Expansions of Taylor series type for linear differential operators. Bull. Math. No. 9

(1983), 1--27. (Reviewer: Robert Carlson) 47E05 (47D05)

[44] 84h:26023 Okikiolu, G. O. Jensen-type convex function inequalities involving positive linear operators. Bull. Math.

1981/82, no. 5, 31--47. 26D20 (46E30 47B38)

[45] 84g:47037 Okikiolu, G. O. Semigroups of operators generated by linear differential operators---representations of

linear multiplicative and differential operators. Bull. Math. No. 8 (1983), 1--48. (Reviewer: S. Newberger) 47D05 (47E05)

[46] 84e:42015 Okikiolu, G. O. Representations of integrals involving homogeneous functions. Bull. Math. 1981/82,

no. 5, 48--63. (Reviewer: M. Cotlar) 42A38

[47] 84b:47051b Okikiolu, G. O. Correction: "Generations of `convolution semigroups' of operators and functions by

parameter integrals". Bull. Math. 1982, no. 7, 64. (Reviewer: A. B. Buche) 47D05 (44A35)

[48] 84b:47051a Okikiolu, G. O. Generations of "convolution semigroups" of operators and functions by parameter

integrals. Bull. Math. 1981/82, no. 6, 1--29. (Reviewer: A. B. Buche) 47D05 (44A35)

[49] 84a:44003 Okikiolu, G. O. Convolution and multiplier identities for Hankel-type operators. Bull. Math. 1981/82,

no. 4, 50--68. (Reviewer: A. Schwartz) 44A15

[50] 83m:47026 Okikiolu, G. O. Extreme functions of bounded linear operators in $L\sp{p}$-spaces. Bull. Math.

1981/82, no. 6, 53--67. (Reviewer: A. R. Sourour) 47B37

[51] 83k:46032b Okikiolu, G. O. Multiple and function space parameter interpolation theorems for positive and maximal

operators. II. Bull. Math. 1981/82, no. 4, 17--39. (Reviewer: Gunnar Sparr) 46E30 (46M35)

[52] 83k:46032a Okikiolu, G. O. Multiple and function space parameter interpolation theorems for positive and maximal

operators. I. Bull. Math. 1981/82, no. 4, 1--16. (Reviewer: Gunnar Sparr) 46E30 (46M35)

[53] 83h:47020 Okikiolu, G. O. Differentiation of $L\sp{p}$-norms of linear expressions and representations of isometric

operators in $L\sp{p}$-spaces. Bull. Math. 1981/82, no. 5, 1--30. (Reviewer: Peter Dodds) 47B38 (46E30)

[54] 83h:44014 Okikiolu, G. O. Weighted inequalities for convolutions: conjugate space estimates. Bull. Math. 1981/82,

no. 2, 62--108. (Reviewer: Ron A. Kerman) 44A35

[55] 83g:46028 Okikiolu, G. O. Extensions of interpolation theorems for linear operators to multiple parameter cases.

Bull. Math. 1981/82, no. 4, 40--49. (Reviewer: Colin Bennett) 46E30 (46M35)

[56] 83c:47005 Okikiolu, G. O. Product identities involving resolvents of differential operators. Bull. Math. 1981/82,

no. 2, 2--61. (Reviewer: Philip Brenner) 47A05 (47E05)

[57] 82i:44007 Okikiolu, G. O. Weighted form of a general inequality. Bull. Math. 1981/82, no. 1, 85--95. (Reviewer:

Philip Heywood) 44A35 (26D10)

[58] 82i:44006 Okikiolu, G. O. Weighted inequalities for convolutions and homogeneous convolutions. Bull. Math.

1981/82, no. 1, 48--84. (Reviewer: Philip Heywood) 44A35 (26D10)

[59] 82i:44005 Okikiolu, G. O. Representations of integrals and convolutions of radial functions. Bull. Math. 1981/82, no. 1, 2--47. (Reviewer: Philip Heywood) 44A35

**Okikiolu, G. O.** *Multidimensional integrals involving
radial functions and functions of inner products,* Bull. Math.
No. **16** (1985), 1--21. 42B10

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