An extended inequality for the maximal function
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- by Richard J. Bagby PDF
- Proc. Amer. Math. Soc. 48 (1975), 419-422 Request permission
Abstract:
Fefferman and Stein [3] have proved an ${L^p}$ inequality for the Hardy-Littlewood maximal function applied to functions taking values in a sequence space ${l^p}$. This note extends their theorem to functions taking values in a mixed ${L^p}$ space. An application to mixed estimates for Riesz potentials is given.References
- David R. Adams and Richard J. Bagby, Translation-dilation invariant estimates for Riesz potentials, Indiana Univ. Math. J. 23 (1973/74), 1051–1067. MR 348471, DOI 10.1512/iumj.1974.23.23086
- A. Benedek and R. Panzone, The space $L^{p}$, with mixed norm, Duke Math. J. 28 (1961), 301–324. MR 126155
- C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107–115. MR 284802, DOI 10.2307/2373450
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 419-422
- MSC: Primary 46E40; Secondary 46A45
- DOI: https://doi.org/10.1090/S0002-9939-1975-0370171-X
- MathSciNet review: 0370171