On Hollenbeck-Verbitsky conjecture for $4/3 < p < 2$

arXiv - MATH - Complex Variables Pub Date : 2024-08-30 DOI:arxiv-2408.17093

Vladan Jaguzović

引用次数: 0

Abstract

Let $P_+$ be the Riesz's projection operator and let $P_-=I-P_+.$ We find best estimates of the expression $\left\lVert \left( \left\lvert P_+f \right\rvert ^s + \left\lvert P_-f \right\rvert ^s \right) ^{1/s} \right\rVert _p $ in terms of Lebesgue p-norm of the function $f \in L^p(\mathbf{T})$ for $p \in (4/3,2)$ and $0 < s \leq \frac{p}{p-1},$ thus extending results from \cite{Melentijevic_2022} and \cite{Melentijevic_2023}, where the mentioned range is not considered.

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关于 $4/3 < p < 2$ 的霍伦贝克-韦尔比茨基猜想

让（P_+）成为里兹投影算子，让（P_-=I-P_+.\）成为里兹投影算子。我们可以找到表达式 $left\lVert \left( \left\lvert P_+f\right\rvert ^s + \left\lvert P_-f \right\rvert ^s \right) ^{1/s} 的最佳估计值。\rightr Vert_p) in terms of Lebesgue p-norm of the function \(f \in L^p(\mathbf{T})$ for$p \in (4/3,2)$ and $0 < s \leq \frac{p}{p-1}、$从而扩展了来自\cite{Melentijevic_2022}和\cite{Melentijevic_2023}的结果，在这两个结果中没有考虑提到的范围。

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arXiv - MATH - Complex Variables

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