Beyond local maximal operators
Hannes Luiro, Antti V. V\"ah\"akangas
TL;DR
This paper establishes sharp boundedness results for generalized local maximal operators acting between fractional weighted Sobolev spaces, with applications to capacities and differentiation of Sobolev functions.
Contribution
It provides new sharp boundedness theorems for generalized local maximal operators between fractional weighted Sobolev spaces, extending previous results.
Findings
Sharp boundedness results for generalized local maximal operators
Boundedness between well-known fractional Sobolev spaces derived
Applications to capacities and Lebesgue differentiation of Sobolev functions
Abstract
We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete boundedness results between well known fractional Sobolev spaces are derived as consequences of our main result. We also apply our boundedness results by studying both generalized neighbourhood capacities and the Lebesgue differentiation of fractional weighted Sobolev functions.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Harmonic Analysis Research · Differential Equations and Boundary Problems