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June, 2022 On Some Properties of Dyadic Operators
Heng Gu, Qingying Xue, Kôzô Yabuta
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Taiwanese J. Math. 26(3): 521-544 (June, 2022). DOI: 10.11650/tjm/211101

Abstract

In this paper, the objects of our investigation are some dyadic operators, including dyadic shifts, multilinear paraproducts and multilinear Haar multipliers. We mainly focus on the continuity and compactness of these operators. First, we consider the continuity properties of these operators. Then, by the Fréchet–Kolmogorov–Riesz–Tsuji theorem, the non-compactness properties of these dyadic operators will be studied. Moreover, we show that their commutators are compact with $\operatorname{CMO}$ functions, which is quite different from the non-compactness properties of these dyadic operators. These results are similar to those for Calderón–Zygmund singular integral operators.

Funding Statement

The authors were supported partly by NSFC (No. 11871101), 111 Project and the National Key Research and Development Program of China (Grant No. 2020YFA0712900). The third author was supported partly by Grant-in-Aid for Scientific Research (C) Nr. 15K04942, Japan Society for the Promotion of Science.

Acknowledgments

The authors want to express their sincere thanks to the referee for his or her valuable remarks and suggestions, which made this paper more readable.

Citation

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Heng Gu. Qingying Xue. Kôzô Yabuta. "On Some Properties of Dyadic Operators." Taiwanese J. Math. 26 (3) 521 - 544, June, 2022. https://doi.org/10.11650/tjm/211101

Information

Received: 7 May 2021; Revised: 5 November 2021; Accepted: 15 November 2021; Published: June, 2022
First available in Project Euclid: 21 November 2021

Digital Object Identifier: 10.11650/tjm/211101

Subjects:
Primary: 42B20 , 47G10

Keywords: commutators of Haar multipliers , compactness , continuity , dyadic shifts , Haar multipliers , paraproducts

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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Vol.26 • No. 3 • June, 2022
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