Abstract
In this paper, we introduce Morrey-Herz spaces \(M\dot K_{q,p( \cdot )}^{\alpha ( \cdot ),\lambda } (\mathbb{R}^n )\) with variable exponents α(·) and p(·), and prove the boundedness of multilinear Calderón-Zygmund singular operators on the product of these spaces.
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Almeida, A., Drihem, D.: Maximal, potential and singular type operators on Herz spaces with variable exponents. J. Math. Anal. Appl., 394, 781–795 (2012)
Curbera, G., García-Cuerva, J., Martell, J., et al.: Extrapolation with weights, rearrangement-invariant function spaces.modular inequalities and applications to singular integrals. Adv. Math., 203, 256–318 (2006)
Diening, L., Harjulehto, P., Hasto, P., et al.: Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Math., No. 2017, Springer, 2011
Grafakos, L., Torres, R.: Multilinear Calderón-Zygmund theory. Adv. Math., 165, 124–164 (2002)
Herz, C.: Lipschitz spaces and Berstein’s theorem on absolutely convergent Fourier transforms. J. Math. Mech., 18, 283–324 (1968)
Huang, A., Xu, J. S.: Multilinear singular integrals and commutators in variable exponent Lebesgue spaces. Appl. Math. J. Chinese Univ., 25(1), 69–77 (2010)
Izuki, M.: Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization. Anal. Math., 36, 33–50 (2010)
Izuki, M.: Fractional integrals on Herz-Morrey spaces with variable exponent. Hiroshima Math. J., 40, 343–355 (2010)
Kováčik, O., Rákosník, J.: On spaces L p (x) and W k,p (x). Czechoslovak Math. J., 41, 592–618 (1991)
Lu, S. Z., Yang, D. C., Hu, G.: Herz Type Spaces and Their Applications, Science Press, Beijing, 2008
Tao, X. X., Zhang, H. H.: On the boundedness of multilinear operators on weighted Herz-Morrey spaces. Taiwanese J. Math., 15(4), 1527–1543 (2011)
Tao, X. X., Yu, X., Zhang, H. H.: Multilinear Calderón Zygmund operators on variable exponent Morrey spaces over domains. Appl. Math. J. Chinese Univ., 26(2), 187–197 (2011)
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Supported by National Natural Science Foundation of China (Grant Nos. 11271209 and 11371370) and Natural Science Foundation of Nantong University (Grant No. 11ZY002)
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Lu, Y., Zhu, Y.P. Boundedness of multilinear Calderón-Zygmund singular operators on Morrey-Herz spaces with variable exponents. Acta. Math. Sin.-English Ser. 30, 1180–1194 (2014). https://doi.org/10.1007/s10114-014-3410-2
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DOI: https://doi.org/10.1007/s10114-014-3410-2