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Weighted Lp-inequalities for multi-parameter Riesz type potentials and strong fractional maximal operators

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Abstract

We prove weighted Lp-inequalities for multi-parameter Riesz type potentials, strong fractional maximal operators and their dyadic counterparts. Our proofs avoid the Good-λ inequalities used earlier in the Rm-case and are based on our integrated multi-parameter summation by parts lemma, that might be of independent interest.

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Authors and Affiliations

  1. Department of Mathematics and Mathematical Statistics, University of Umeå, 901 87, Umeå, Sweden

    Tord Sjödin

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  1. Tord Sjödin
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Correspondence to Tord Sjödin.

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Sjödin, T. Weighted Lp-inequalities for multi-parameter Riesz type potentials and strong fractional maximal operators. Math. Ann. 337, 317–333 (2007). https://doi.org/10.1007/s00208-006-0035-5

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  • DOI: https://doi.org/10.1007/s00208-006-0035-5

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