Real analysis without using the Hardy–Littlewood maximal operator
Copyright policy )Real analysis without using the Hardy–Littlewood maximal operator
In the paper, the author focuses on a sampling theorem that is one of the real analytic topics independent of the Hardy-Littlewood maximal operator \(\mathcal M \). He/She specifically explains the following two results: (1) Extension of series corresponding to the sampling theorem to analytic functions (Section 3 [\textit{M. Izuki}, Complex Anal. Oper. Theory 3, No. 4, 867--880 (2009; Zbl 1181.42038); \textit{A. I. Zayed} and \textit{G. G. Walter}, Complex Variables, Theory Appl. 29, No. 3, 265--276 (1996; Zbl 0852.30004)]). (2) A sampling theorem in general function spaces (Section 6 [\textit{M. Izuki} and \textit{Y. Sawano}, Tokyo J. Math. 36, No. 1, 131--145 (2013; Zbl 1348.42021)]).
- Tokyo City University Japan
sampling theorem, Maximal functions, Littlewood-Paley theory, \(\varphi\)-transform, Inequalities for sums, series and integrals, Nontrigonometric harmonic analysis involving wavelets and other special systems, Sampling theory in information and communication theory, analytic function, wavelet theory, Hardy-Littlewood maximal operator
sampling theorem, Maximal functions, Littlewood-Paley theory, \(\varphi\)-transform, Inequalities for sums, series and integrals, Nontrigonometric harmonic analysis involving wavelets and other special systems, Sampling theory in information and communication theory, analytic function, wavelet theory, Hardy-Littlewood maximal operator
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