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Bilinear \(\theta \)-type Calderón–Zygmund operator and its commutator on non-homogeneous weighted Morrey spaces

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The main purpose of this paper is to establish the boundedness of bilinear \(\theta \)-type Calderón–Zygmund operator \(T_{\theta }\) and its commutator \([b_{1},b_{2},T_{\theta }]\) generated by the function \(b_{i}\in \widetilde{\mathrm {RBMO}}(\mu )\) with \(i=1,2\) and \(T_{\theta }\) on weighted Morrey space \(L^{p,\kappa ,\varrho }(\omega )\) and weighted weak Morrey space \(WL^{p,\kappa ,\varrho }(\omega )\) over non-homogeneous metric measure space. Under assumption that \(\omega \) satisfies weighted integral conditions, the author proves that \(T_{\theta }\) is bounded from weighted weak Morrey space \(WL^{p,\kappa ,\varrho }(\omega )\) into weighted Morrey space \(L^{p,\kappa ,\varrho }(\omega )\) with \(1\le p<\infty \). In addition, via the sharp maximal function, the boundedness of the commutator \([b_{1},b_{2},T_{\theta }]\) on the weighted Morrey space \(L^{p,\kappa ,\varrho }(\omega )\) is also obtained.

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Acknowledgements

The author thanks the referees for the helpful comments and suggestions that contributed to the improvement of this paper.

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  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, Gansu, People’s Republic of China

    Guanghui Lu

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  1. Guanghui Lu
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The research is supported by the Innovation Capacity Improvement Project for Colleges and Universities of Gansu Province (2020A-010) and the Doctoral Scientific Research Foundation of Northwest Normal University (0002020203).

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Lu, G. Bilinear \(\theta \)-type Calderón–Zygmund operator and its commutator on non-homogeneous weighted Morrey spaces. RACSAM 115, 16 (2021). https://doi.org/10.1007/s13398-020-00955-8

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