-Regularity and Weights for Operators Between -Spaces

  • Enrique A. Sánchez Pérez

    Universitat Politècnica de València, Spain
  • Pedro Tradacete

    Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain
$p$-Regularity and Weights for Operators Between $L^p$-Spaces cover

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Abstract

We explore the connection between -regular operators on Banach function spaces and weighted -estimates. In particular, our results focus on the following problem. Given finite measure spaces and , let be an operator defined from a Banach function space and taking values on for in certain family of weights we analyze the existence of a bounded family of weights such that for every there is in such a way that is continuous uniformly on . A condition for the existence of such a family is given in terms of -regularity of the integration map associated to a certain vector measure induced by the operator .

Cite this article

Enrique A. Sánchez Pérez, Pedro Tradacete, -Regularity and Weights for Operators Between -Spaces. Z. Anal. Anwend. 39 (2020), no. 1, pp. 41–65

DOI 10.4171/ZAA/1650