A Generalization of Littlewood-Paley Type Inequality for Evolution Systems Associated with Pseudo Differential Operators
Year: 2025
Type: preprint
Abstract: In this paper, we first prove that the Littlewood-Paley $g$-function, related to the convolution corresponding to the composition of pseudo-differential operator and evolution system associated with pseudo-differential operators, is a bounded operator from $L^{q}((a,b)\times \mathbb{R}^{d};V)$ with a Hilbert space $V$ into $L^{q}((a,b)\times \mathbb{R}^{d})$. Secondly, we prove that the sharp function of the Littlewood-Paley $g$-function is bounded by some maximal function. Finally, by applying Fefferman-Stein theorem and Hardy-Littlewood maximal theorem, we prove the Littlewood-Paley type inequality for evolution systems associated with pseudo-differential operators.
Source: arXiv (Cornell University)
Authors: Ji, Un Cig, Kim, Jae Hun
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979297774
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