Matrix dilation and Hausdorff operators on modulation spaces
Weichao Guo, Jiangkun Luo, Guoping Zhao
TL;DR
This paper investigates the behavior of matrix dilation and Hausdorff operators on modulation spaces, providing asymptotic estimates and boundedness conditions, advancing understanding of these operators in harmonic analysis.
Contribution
The paper establishes asymptotic estimates for matrix dilation operators and characterizes the boundedness of Hausdorff operators on modulation spaces, extending previous theoretical frameworks.
Findings
Derived asymptotic estimates for matrix dilation operators
Established boundedness criteria for Hausdorff operators on modulation spaces
Revisited the definition of Hausdorff operators for this context
Abstract
In this paper, we establish the asymptotic estimates for the norms of the matrix dilation operators on modulation spaces. As an application, we study the boundedness on modulation spaces of Hausdorff operators. The definition of Hausdorff operators are also revisited for fitting our study.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Approximation Theory and Sequence Spaces · Advanced Harmonic Analysis Research