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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 9
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Research Article

Weak type estimates of commutators on Herz type spaces with variable exponent

Pages 3264-3283 | Received 04 Aug 2020, Accepted 20 Oct 2020, Published online: 04 Nov 2020

References

  • Coifman R, Rochberg R, Weiss G. Factorization theorems for Hardy spaces on several variables. Ann Math. 1976;103:611–635.
  • Agarwal RP, Gala S, Ragusa MA. A regularity criterion in weak spaces to Boussinesq equations. Math. 2020;8:920.
  • Lu S. Some results and problems on commutators. Front Math China. 2011;6:821–833.
  • Ragusa MA, Tachikawa A. Regularity for minimizers for functionals of double phase with variable exponents. Adv Nonlinear Anal. 2020;9:710–728.
  • Shamoyan R, Mihic O. On some new sharp embedding theorems for multifunctional Herz type and Bergman type spaces in pseudoconvex domains. Filomat. 2019;33:5677–5690.
  • Wang F, Yang D, Yang S. Applications of Hardy spaces associated with ball quasi-Banach function spaces. Results Math. 2020;75:1–58.
  • Lu S, Yang D. The continuity of commutators on Herz-type spaces. Michigan Math J. 1997;44:255–281.
  • Cruz-Uribe D, Fiorenza A, Martell J, et al. The boundedness of classical operators on variable Lp spaces. Ann Acad Sci Fen Math. 2006;31:239–264.
  • Izuki M. Boundedness of commutators on Herz spaces with variable exponent. Rend Del Circolo Mate Di Palermo. 2010;59:199–213.
  • Wang H. Boundedness of commutators on Herz-type Hardy spaces with variable exponent. Jordan J Math Stat. 2016;9:17–30.
  • Wang H. The continuity of commutators on Herz-type Hardy spaces with variable exponent. Kyoto J Math. 2016;56:559–573.
  • Wang H. Commutators of homogeneous fractional integrals on Herz-type Hardy spaces with variable exponent. J Contemp Math Anal. 2017;52:134–143.
  • Wang H. Commutators of singular integral operator on Herz-type Hardy spaces with variable exponent. J Korean Math Soc. 2017;54:713–732.
  • Wang H, Liu Z. Boundedness of singular integral operators on weak Herz type spaces with variable exponent. Ann Funct Anal. 2020;11:1108–1125.
  • Cruz-Uribe D, Fiorenza A. Variable Lebesgue spaces: foundations and harmonic analysis(Applied and numerical harmonic analysis). Heidelberg: Springer; 2013.
  • Cruz-Uribe D, Fiorenza A, Neugebauer C. The maximal function on variable Lp spaces. Ann Acad Sci Fenn Math. 2003;28:223–238.
  • Kováčik O, Rákosník J. On spaces Lp(x) and Wk,p(x). Czechoslovak Math J. 1991;41:592–618.
  • Izuki M. Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization. Anal Math. 2010;36:33–50.
  • Diening L, Harjulehto P, Hästö P, et al. Lebesgue and Sobolev spaces with variable exponents. Heidelberg: Springer; 2011. (Lecture Notes in Math; 2017).
  • Wang H, Liu Z. The Herz-type Hardy spaces with variable exponent and their applications. Taiwanese J Math. 2012;16:1363–1389.
  • Ho K. John–Nirenbeg inequalities on Lebesgue spaces with variable exponents. Taiwanese J Math. 2014;18:1107–1118.
  • Zhang P, Wu J. Commutators of the fractional maximal function on variable exponent Lebesgue spaces. Czechoslovak Math J. 2014;64:183–197.
  • Liu Z. Boundedness of commutators of Calderón–Zygmund singular integral operators on Herz-type Hardy spaces. Adv Math (China). 2001;30:447–458.
  • Capone C, Cruz-Uribe D, Fiorenza A. The fractional maximal operator and fractional integrals on variable Lp spaces. Rev Mat Iberoamericana. 2007;23:743–770.

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