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Two-Weight Norm Estimates for Multilinear Fractional Integrals in Classical Lebesgue Spaces

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Abstract

We derive criteria governing two-weight estimates for multilinear fractional integrals and appropriate maximal functions. The two and one weight problems for multi(sub)linear strong fractional maximal operators are also studied; in particular, we derive necessary and sufficient conditions guaranteeing the trace type inequality for this operator. We also establish the Fefferman-Stein type inequality, and obtain one-weight criteria when a weight function is of product type. As a consequence, appropriate results for multilinear Riesz potential operator with product kernels follow.

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Authors and Affiliations

  1. A. Razmadze Mathematical Institute I. Javakhishvili Tbilisi State University 6, Tamarashvili Str., Tbilisi, Georgia, 0177, USA

    Vakhtang Kokilashvili

  2. I. Javakhishvili Tbilisi State University, International Black Sea University 3 Agmashenebeli Ave., Tbilisi, Georgia, 0131, USA

    Vakhtang Kokilashvili

  3. Faculty of Mathematics and Computer Science Adam Mickiewicz University Poznań and Institute of Mathematics Polish Academy of Sciences (Poznań branch) Umultowska, 87,61-614, Poznań, Poland

    Mieczysław Mastyło

  4. A. Razmadze Mathematical Institute I. Javakhishvili Tbilisi State University 6, Tamarashvili Str., Tbilisi, Georgia, 0177, USA

    Alexander Meskhi

  5. Department of Mathematics, Faculty of Informatics and Control Systems Georgian Technical University 77, Kostava St., Tbilisi, Georgia, USA

    Alexander Meskhi

Authors
  1. Vakhtang Kokilashvili
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  2. Mieczysław Mastyło
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  3. Alexander Meskhi
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Correspondence to Vakhtang Kokilashvili.

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Kokilashvili, V., Mastyło, M. & Meskhi, A. Two-Weight Norm Estimates for Multilinear Fractional Integrals in Classical Lebesgue Spaces. FCAA 18, 1146–1163 (2015). https://doi.org/10.1515/fca-2015-0066

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  • DOI: https://doi.org/10.1515/fca-2015-0066

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