On the radial and nontangential maximal functions for the disc

Author:
Richard L. Wheeden

Journal:
Proc. Amer. Math. Soc. **42** (1974), 418-422

MSC:
Primary 30A78

MathSciNet review:
0333194

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Abstract: Positive powers of the radial and nontangential maximal functions of a function which is harmonic or analytic in the unit disc are shown to have equivalent integrals with respect to Borel measures satisfying the growth condition for every interval *I*.

**[1]**D. L. Burkholder and R. F. Gundy,*Boundary behaviour of harmonic functions in a half-space and Brownian motion*, Ann. Inst. Fourier (Grenoble)**23**(1973), no. 4, 195–212 (English, with French summary). MR**0365691****[2]**D. L. Burkholder and R. F. Gundy,*Distribution function inequalities for the area integral*, Studia Math.**44**(1972), 527–544. Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, VI. MR**0340557****[3]**Charles Fefferman and Benjamin Muckenhoupt,*Two nonequivalent conditions for weight functions*, Proc. Amer. Math. Soc.**45**(1974), 99–104. MR**0360952**, 10.1090/S0002-9939-1974-0360952-X**[4]**C. Fefferman and E. M. Stein,*𝐻^{𝑝} spaces of several variables*, Acta Math.**129**(1972), no. 3-4, 137–193. MR**0447953****[5]**R. F. Gundy and R. L. Wheeden,*Weighted integral inequalities for the nontangential maximal function, Lusin area integral, and Walsh-Paley series*, Studia Math.**49**(1973/74), 107–124. MR**0352854****[6]**Miguel de Guzmán,*A covering lemma with applications to differentiability of measures and singular integral operators*, Studia Math.**34**(1970), 299–317. (errata insert). MR**0264022****[7]**Elias M. Stein,*Singular integrals and differentiability properties of functions*, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR**0290095**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1974-0333194-1

Article copyright:
© Copyright 1974
American Mathematical Society