p-regularity and weights for operators between L^p-spaces

2018/03/28 by Pérez, Enrique A. Sánchez, Tradacete, Pedro
#46B42 #46E30 #47B10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1803.10652

Abstract

We explore the connection between p-regular operators on Banach function spaces and weighted p-estimates. In particular, our results focus on the following problem. Given finite measure spaces μ and ν, let T be an operator defined from a Banach function space X(ν) and taking values on L^p (v d μ) for v in certain family of weights V⊂ L¹(μ)₊: we analyze the existence of a bounded family of weights W⊂ L¹(ν)₊ such that for every v∈ V there is w ∈ W in such a way that T:L^p(w d ν) → L^p(v d μ) is continuous uniformly on V. A condition for the existence of such a family is given in terms of p-regularity of the integration map associated to a certain vector measure induced by the operator T.

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