Variable exponent fractional integrals in the limiting case alpha(x)p(x) equivalent to n on quasimetric measure spaces

We show that the fractional operator I-alpha(center dot), of variable order on a bounded open set in Omega, in a quasimetric measure space (X, d, mu) in the case alpha(x)p(x) = n (where n comes from the growth condition on the measure mu), is bounded from the variable exponent Lebesgue space L-p(cen...

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Bibliographic Details
Main Author: Samko, Stefan (author)
Format: article
Language:eng
Published: 2021
Subjects:
Riesz potential
Variable exponent spaces
Sobolev type theorem
BMO results
Quasimetric measure space
Mathematics
Online Access:http://hdl.handle.net/10400.1/16553
Country:Portugal
Oai:oai:sapientia.ualg.pt:10400.1/16553
Description
Summary:We show that the fractional operator I-alpha(center dot), of variable order on a bounded open set in Omega, in a quasimetric measure space (X, d, mu) in the case alpha(x)p(x) = n (where n comes from the growth condition on the measure mu), is bounded from the variable exponent Lebesgue space L-p(center dot)(Omega) into BMO(Omega) under certain assumptions on p(x) and alpha(x).

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