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January 2020 Oscillatory integrals with variable Calderón-Zygmund kernel on vanishing generalized Morrey spaces
V. S. Guliyev, A. Ahmadli, S. E. Ekincioglu
Tbilisi Math. J. 13(1): 69-82 (January 2020). DOI: 10.32513/tbilisi/1585015221

Abstract

In this paper, the authors investigate the boundedness of the oscillatory singular integrals with variable Calderón-Zygmund kernel on generalized Morrey spaces $M^{p,\varphi}(\mathbb R^n)$ and the vanishing generalized Morrey spaces $VM^{p,\varphi}(\mathbb R^n)$. When $1<p<\infty$ and $(\varphi_1,\varphi_2)$ satisfies some conditions, we show that the oscillatory singular integral operators $T_{\lambda}$ and $T_{\lambda}^{*}$ are bounded from $M^{p,\varphi_1}(\mathbb R^n)$ to $M^{p,\varphi_2}(\mathbb R^n)$ and from $VM^{p,\varphi_1}(\mathbb R^n)$ to $VM^{p,\varphi_2}(\mathbb R^n)$. Meanwhile, the corresponding result for the oscillatory singular integrals with standard Calderón-Zygmund kernel are established.

Funding Statement

The research of V. Guliyev was partially supported by the Grant of 1st Azerbaijan-Russia Joint Grant Competition (Agreement Number No. EIF-BGM-4-RFTF-1/2017-21/01/1).

Acknowledgment

We thank the referee(s) for careful reading the paper and useful comments.

Citation

Download Citation

V. S. Guliyev. A. Ahmadli. S. E. Ekincioglu. "Oscillatory integrals with variable Calderón-Zygmund kernel on vanishing generalized Morrey spaces." Tbilisi Math. J. 13 (1) 69 - 82, January 2020. https://doi.org/10.32513/tbilisi/1585015221

Information

Received: 4 September 2019; Accepted: 4 December 2019; Published: January 2020
First available in Project Euclid: 24 March 2020

zbMATH: 07200153
MathSciNet: MR4079451
Digital Object Identifier: 10.32513/tbilisi/1585015221

Subjects:
Primary: 42B20
Secondary: 42B25, 42B35

Rights: Copyright © 2020 Tbilisi Centre for Mathematical Sciences

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Vol.13 • No. 1 • January 2020
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