Characterization of Carleson measures by the Hausdorff-Young property
Sergey Sadov
TL;DR
This paper establishes a characterization of Carleson measures through the Hausdorff-Young inequality for Laplace transforms of Lp functions, linking measure properties with integral inequalities in complex analysis.
Contribution
It provides a new necessary and sufficient condition for Carleson measures based on the Hausdorff-Young property of Laplace transforms of Lp functions.
Findings
Laplace transform of Lp functions satisfies Hausdorff-Young inequality with a weight if and only if the weight is a Carleson measure.
Characterization of Carleson measures via integral inequalities in the complex half-plane.
Bridges measure theory and harmonic analysis through the Hausdorff-Young property.
Abstract
It is shown that the Laplace transform of an Lp (1<p<=2) function defined on the positive semiaxis satisfies the Hausdorff-Young type inequality with a positive weight in the right complex half-plane if and only if the weight is a Carleson measure.
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