Perron树几何极大算子的应用

Pub Date : 2022-04-06 DOI:10.4064/cm8693-8-2022

A. Gauvan

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引用次数: 4

摘要

我们刻画了几何极大算子M a,b与基ba,b (a,b > 0)相关联的L p (r2)有界性，该算子由矩形R组成，其偏心率和方向为(e R， ω R) = (cid:18) 1 n a， π 4 n b (cid:19)，对于某些n∈n∗。证明涉及到在[12]中构造的广义Perron树。

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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Application of Perron trees to geometric maximal operators

We characterize the L p ( R 2 ) boundeness of the geometric maximal operator M a,b associated to the basis B a,b ( a, b > 0) which is composed of rectangles R whose eccentricity and orientation is of the form ( e R , ω R ) = (cid:18) 1 n a , π 4 n b (cid:19) for some n ∈ N ∗ . The proof involves generalized Perron trees , as constructed in [12].

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