-Regularity and Weights for Operators Between -Spaces
Enrique A. Sánchez Pérez
Universitat Politècnica de València, SpainPedro Tradacete
Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain
![$p$-Regularity and Weights for Operators Between $L^p$-Spaces cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-zaa-volume-39-issue-1.png&w=3840&q=90)
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