The Hardy Operator and Boyd Indices
Stephen J. Montgomery-Smith
TL;DR
This paper establishes precise criteria based on Boyd indices for when the Hardy operator is bounded on rearrangement invariant quasi-Banach spaces, advancing understanding of operator behavior in these function spaces.
Contribution
It provides necessary and sufficient conditions for the Hardy operator's boundedness using Boyd indices, a novel characterization in the context of quasi-Banach spaces.
Findings
Hardy operator boundedness characterized by Boyd indices
Necessary and sufficient conditions derived
Enhanced understanding of operator behavior in quasi-Banach spaces
Abstract
We give necessary and sufficient conditions for the Hardy operator to be bounded on a rearrangement invariant quasi-Banach space in terms of its Boyd indices.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Holomorphic and Operator Theory · Mathematical Analysis and Transform Methods