解析投影和共解析投影的反向里兹型不等式中的最佳常数

arXiv - MATH - Complex Variables Pub Date : 2024-08-05 DOI:arxiv-2408.02453

Petar Melentijević

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摘要

\开始{摘要｝设 $P_+$ 为里氏投影算子，设 $P_-= I- P_+$ 为里氏投影算子。我们考虑以下形式的不等式 $$\|f\|_{L^p(\mathbb{T})}\leq B_{p、s}\|( |P_ + f | ^s + |P_- f |^s) ^{\frac1s}\|_{L^p (\mathbb{T})} $$ 并用尖锐常数$B_{p,s}$来证明它们，其中$s在[p',+\infty)$并且$1本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Best constants in reverse Riesz-type inequalities for analytoc and co-analytic projections

\begin{abstract} Let $P_+$ be the Riesz's projection operator and let $P_-= I - P_+$. We consider the inequalities of the following form $$ \|f\|_{L^p(\mathbb{T})}\leq B_{p,s}\|( |P_ + f | ^s + |P_- f |^s) ^{\frac 1s}\|_{L^p (\mathbb{T})} $$ and prove them with sharp constant $B_{p,s}$ for $s \in [p',+\infty)$ and $1

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arXiv - MATH - Complex Variables

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