Tbilisi Mathematical Journal

Oscillatory integrals with variable Calderón-Zygmund kernel on vanishing generalized Morrey spaces

V. S. Guliyev, A. Ahmadli, and S. E. Ekincioglu

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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.


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).


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

Article information

Tbilisi Math. J., Volume 13, Issue 1 (2020), 69-82.

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

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Mathematical Reviews number (MathSciNet)

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 42B35: Function spaces arising in harmonic analysis

vanishing generalized Morrey space oscillatory integral variable Calderón-Zygmund kernels


Guliyev, V. S.; Ahmadli, A.; Ekincioglu, S. E. Oscillatory integrals with variable Calderón-Zygmund kernel on vanishing generalized Morrey spaces. Tbilisi Math. J. 13 (2020), no. 1, 69--82. doi:10.32513/tbilisi/1585015221. https://projecteuclid.org/euclid.tbilisi/1585015221

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