Convolution in the harmonic Hardy class $h^ p$ with $0<p<1$
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- by Miroslav Pavlović PDF
- Proc. Amer. Math. Soc. 109 (1990), 129-134 Request permission
Abstract:
It is proved that if $u \in {h^p},0 < p < 1$, and $v \in {h^q},q \geq p$, then \[ {M_q}(u * v,r) = 0\left ( {{{(1 - r)}^{1 - 1/p}}} \right ),r \to 1 - ,\] where $u*v$ stands for the convolution of $u$ and $v$.References
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655 G H. Hardy and J. E. Littlewood, Some properties of conjugate functions, J. Reine Angew. Math. 167 (1932), 405-423.
- Miroslav Pavlović, An inequality for the integral means of a Hadamard product, Proc. Amer. Math. Soc. 103 (1988), no. 2, 404–406. MR 943056, DOI 10.1090/S0002-9939-1988-0943056-4
- Miroslav Pavlović, Mean values of harmonic conjugates in the unit disc, Complex Variables Theory Appl. 10 (1988), no. 1, 53–65. MR 946099, DOI 10.1080/17476938808814287
- Joel H. Shapiro, Linear topological properties of the harmonic Hardy spaces $h^p$ for $0<p<1$, Illinois J. Math. 29 (1985), no. 2, 311–339. MR 784526
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 129-134
- MSC: Primary 31A05; Secondary 30D55
- DOI: https://doi.org/10.1090/S0002-9939-1990-1012937-7
- MathSciNet review: 1012937