Grand Lebesgue空间中的复合算子

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2023-02-08 DOI:10.1007/s10476-023-0201-y

A. Karapetyants, M. Lanza de Cristoforis

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引用次数: 0

摘要

设Ω是ℝ有限测度的n。设f是Borel可测函数ℝ 到ℝ. 我们证明了f上复合函数Tf[g]=f o g属于Grand Lebesgue空间Lp），θ（Ω）（当g属于Lp）时）的充要条件。我们还研究了Lp）中复合算子Tf[·]的连续性、一致连续性、Hölder和Lipschitz连续性。

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Composition Operators in Grand Lebesgue Spaces

Let Ω be an open subset of ℝⁿ of finite measure. Let f be a Borel measurable function from ℝ to ℝ. We prove necessary and sufficient conditions on f in order that the composite function T_f[g] = f o g belongs to the Grand Lebesgue space L_p),θ(Ω) whenever g belongs to L_p),θ(Ω).

We also study continuity, uniform continuity, Hölder and Lipschitz continuity of the composition operator T_f[·] in L_p),θ(Ω).

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.