학술논문
Menshov-type theorem for divergence sets of sequences of localized operators.
Document Type
Journal Translation
Author
Grigoryan, M. G. (AR-YER-NDM) AMS Author Profile; Kamont, A. (PL-PAN) AMS Author Profile; Maranjyan, A. A. (AR-YER-NDM) AMS Author Profile
Source
Subject
42 Harmonic analysis on Euclidean spaces -- 42A Harmonic analysis in one variable
42A05Trigonometric polynomials, inequalities, extremal problems
42A20Convergence and absolute convergence of Fourier and trigonometric series
42Harmonic analysis on Euclidean spaces -- 42C Nontrigonometric harmonic analysis
42C40Wavelets and other special systems
42A05
42A20
42
42C40
Language
English
Abstract
The authors construct a function $f\in M[0,1]^d$ such that the sequence $\{U_{\overline{n}}f(x): \overline{n}\in \Bbb N^p\}$ diverges for $x\in D \subset [0,1]^d$ and converges for $x\in [0,1]^d\setminus D $, where $U_{\overline{n}}\:L^1 [0,1]^d \rightarrow M[0,1]^d$, $D$ is a countable set, $U_{\overline{n}}$ is a multi-parameter sequence of suitably localized operators, and $M[0,1]^d$ is the space of bounded functions in $[0,1]^d$.