On a theorem of Hardy and Littlewood on the polydisc

Author:
Hong Oh Kim

Journal:
Proc. Amer. Math. Soc. **97** (1986), 403-409

MSC:
Primary 32A35; Secondary 30D55

DOI:
https://doi.org/10.1090/S0002-9939-1986-0840619-X

MathSciNet review:
840619

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the polydisc version of the theorem of Hardy and Littlewood on the fractional integral: If and if , then with where is the fractional integral of of order .

**[1]**P. L. Duren,*Theory of**spaces*, Academic Press, New York, 1970. MR**0268655 (42:3552)****[2]**T. M. Flett,*The dual of an inequality of Hardy and Littlewood and some related inequalities*, J. Math. Anal. Appl.**38**(1972), 746-765. MR**0304667 (46:3799)****[3]**A. Frazier,*The dual space of**of the polydisc for*, Duke Math. J.**39**(1972), 369-379. MR**0293119 (45:2198)****[4]**G. H. Hardy and J. E. Littlewood,*Some properties of fractional integrals*. II, Math. Z.**34**(1932), 403-439. MR**1545260****[5]**-,*Theorems concerning mean values of analytic or harmonic functions*, Quart. J. Math.**12**(1941), 221-256. MR**0006581 (4:8d)****[6]**B. Jawerth and A. Torchinsky,*On a Hardy and Littlewood imbedding theorem*, preprint.**[7]**H. O. Kim.*Derivatives of Blaschke products*, Pacific J. Math.**114**(1984), 175-191. MR**755488 (85h:30045)****[8]**W. Rudin,*Function theory in polydiscs*, Benjamin, New York, 1969. MR**0255841 (41:501)****[9]**-,*Function theory in the unit ball of*, Springer-Verlag, New York, 1980.**[10]**A. Zygmund,*On the boundary value of functions of several complex variables*. I, Fund. Math.**36**(1949), 207-235. MR**0035832 (12:18b)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0840619-X

Keywords:
Fractional integral,
maximal theorem,
Hardy space

Article copyright:
© Copyright 1986
American Mathematical Society