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On embeddings of spaces of bivariate functions of bounded $p$-variation

By Martin Lind

Abstract

We obtain sharp estimates of the Hardy-Vitali type total $p$-variation of a function of two variables in terms of its mixed modulus of continuity in $L^p([0,1]^2)$. We also investigate various embeddings for mixed norm spaces of bivariate functions whose linear sections have bounded $p$-variation in the sense of Wiene

Topics: Mathematics - Classical Analysis and ODEs, 26A45 (Primary) 26B35, 46E35 (Secondary)
Year: 2012
OAI identifier: oai:arXiv.org:1208.4936

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