A characterization of weighted Sobolev spaces via weighted Riesz bounded variation spaces
Volume 274 / 2024
Studia Mathematica 274 (2024), 287-304
MSC: Primary 26B05; Secondary 26B30, 42B35
DOI: 10.4064/sm230729-14-12
Published online: 23 February 2024
Abstract
We introduce weighted Riesz bounded variation spaces defined on an open subset of $n$-dimensional Euclidean space and use them to characterize weighted Sobolev spaces when the weight belongs to the Muckenhoupt class. As an application, using Rubio de Francia’s extrapolation theory, we obtain a similar characterization of variable exponent Sobolev spaces via variable exponent Riesz bounded variation spaces.
