Abstract
Our aim in the present paper is to prove the boundedness of vector-valued commutators on Herz spaces with variable exponent. In order to obtain the result, we clarify a relation between variable exponent and BMO norms.
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Coifman, R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variables, Ann. Math., (2) 103 (1976), 611–635
Cruz-Uribe, D., Fiorenza, A., Martell, J.M., Pérez, C.: The boundedness of classical operators on variable L p spaces, Ann. Acad. Sci. Fenn. Math., 31 (2006), 239–264
Cruz-Uribe, D., Fiorenza, A., Neugebauer, C.J.:The maximal function on variable L p spaces, Ann. Acad. Sci. Fenn.Math., 28 (2003), 223–238, and 29 (2004), 247–249
Diening, L.: Maximal functions on Musielak-Orlicz spaces and generalized Lebesgue spaces, Bull. Sci. Math., 129 (2005), 657–700
Izuki, M.: Herz and amalgam spaces with variable exponent, the Haar wavelets and greediness of the wavelet system, East J. Approx., 15 (2009), 87–109
Izuki, M.: Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization, to appear in Anal. Math., 36 (2010)
Jiang, Y., Tang, L., Yang, D.: Continuity of commutators on weighted Herz-type spaces, Kyushu J. Math., 53 (1999), 245–263
Yu. Karlovich, A. Yu., Lerner, A.K.: Commutators of singular integrals on generalized L p spaces with variable exponent, Publ. Mat., 49 (2005), 111–125
Kováčik, O., Rákosník, J.: On spaces L p(x) and W k,p(x), Czechoslovak Math., 41(116) (1991), 592–618
Lu, S., Yang, D.: The continuity of commutators on Herz-type spaces, Michigan Math. J., 44 (1997), 255–281
Nekvinda, A.: Hardy-Littlewood maximal operator on L p(x)(ℝn), Math. Inequal. Appl., 7 (2004), 255–265
Pérez, C.: Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function, J. Fourier Anal. Appl., 6 (1997), 743–756
Stein, E.M.: Harmonic Analysis: real-variable methods, orthogornality and oscillatory integrals. Princeton, NJ: Princeton Univ. Press (1993)
Torchinsky, A.: Real-variable methods in harmonic analysis. (Pure Applied Math., 123). New York: Academic Press (1986)
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Izuki, M. Boundedness of commutators on Herz spaces with variable exponent. Rend. Circ. Mat. Palermo 59, 199–213 (2010). https://doi.org/10.1007/s12215-010-0015-1
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DOI: https://doi.org/10.1007/s12215-010-0015-1