Abstract
In this paper, we give some new characterizations of the Lipschitz spaces via the boundedness of commutators associated with the fractional maximal operator, Riesz potential and Calderón–Zygmund operator on generalized Orlicz–Morrey spaces.
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Adams, D.R.: A note on Riesz potentials. Duke Math. J. 42, 765–778 (1975)
Agcayazi, M., Gogatishvili, A., Koca, K., Mustafayev, R.: A note on maximal commutators and commutators of maximal functions. J. Math. Soc. Jpn. 67(2), 581–593 (2015)
Bastero, J., Milman, M., Ruiz, F.J.: Commutators for the maximal and sharp functions. Proc. Am. Math. Soc. 128(11), 3329–3334 (2000)
Calderón, A.P.: Commutators of singular integral operators. Proc. Nat. Acad. Sci. USA 53, 1092–1099 (1965)
Chanillo, S.: A note on commutators. Indiana Univ. Math. J. 31(1), 7–16 (1982)
Coifman, R.R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variables. Ann. Math. 103(3), 611–635 (1976)
Coifman, R.R., Lions, P., Meyer, Y., Semmes, S.: Compensated compactness and Hardy spaces. J. Math. Pures Appl. 72, 247–286 (1993)
Deringoz, F., Guliyev, V.S., Samko, S.: Boundedness of maximal and singular operators on generalized Orlicz-Morrey spaces. Oper. Theory, Oper. Algebras Appl. Series: Operator Theory: Adv. Appl. 242, 139–158 (2014)
DeVore, R.A., Sharpley, R.C.: Maximal functions measuring smoothness. Mem. Am. Math. Soc. 47(293), 115 (1984)
Deringoz, F., Guliyev, V.S., Hasanov, S.G.: Characterizations for the Riesz potential and its commutators on generalized Orlicz-Morrey spaces. J. Inequal. Appl. 248, 22 (2016)
Deringoz, F., Guliyev, V.S., Hasanov, S.G.: A characterization for Adams-type boundedness of the fractional maximal operator on generalized Orlicz-Morrey spaces. Integral Transforms Spec. Funct. 28(4), 284–299 (2017)
Ding, Y.: A characterization of BMO via commutators for some operators. Northeast Math. J. 13(4), 422–432 (1997)
Guliyev, V.S., Deringoz, F.: On the Riesz potential and its commutators on generalized Orlicz-Morrey spaces. J. Funct. Spaces 617414, 11 (2014)
Guliyev, V.S., Deringoz, F.: Boundedness of fractional maximal operator and its commutators on generalized Orlicz-Morrey spaces. Complex Anal. Oper. Theory 9(6), 1249–1267 (2015)
Guliyev, V.S., Deringoz, F., Hasanov, S.G.: Fractional maximal function and its commutators on Orlicz spaces, Anal. Math. Phys. https://doi.org/10.1007/s13324-017-0189-1
Janson, S.: Mean oscillation and commutators of singular integral operators. Ark. Mat. 16, 263–270 (1978)
Nakai, E.: Recent topics of fractional integrals. Sugaku Expositions 20(2), 215–235 (2007)
Paluszyński, M.: Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss. Indiana Univ. Math. J. 44(1), 1–17 (1995)
Peetre, J.: On the theory of \(M_{p,\lambda }\). J. Funct. Anal. 4, 71–87 (1969)
Shi, S., Lu, S.: Some characterizations of Campanato spaces via commutators on Morrey spaces. Pac. J. Math. 264(1), 221–234 (2013)
Zhang, P., Wu, J.L.: Commutators of the fractional maximal functions. Acta Math. Sinica (Chin. Ser.) 52, 1235–1238 (2009)
Zhang, P., Wu, J.L.: Commutators of the fractional maximal function on variable exponent Lebesgue spaces. Czechoslovak Math. J. 64(139), 183–197 (2014)
Zhang, P.: Characterization of Lipschitz spaces via commutators of the Hardy-Littlewood maximal function. C. R. Acad. Sci. Paris 355(3), 336–344 (2017)
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The authors are grateful to the referee for careful reading of the paper and valuable suggestions and comments.
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The research of V.S. Guliyev was partially supported by the grant of the 1st Azerbaijan–Russia Joint Grant Competition (Agreement number no. EIF-BGM-4-RFTF-1/2017-21/01/1) and by the Ministry of Education and Science of the Russian Federation (Agreement number no. 02.a03.21.0008). The research of F. Deringoz was partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A4.17.009).
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Guliyev, V.S., Deringoz, F. Some Characterizations of Lipschitz Spaces via Commutators on Generalized Orlicz–Morrey Spaces. Mediterr. J. Math. 15, 180 (2018). https://doi.org/10.1007/s00009-018-1226-5
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DOI: https://doi.org/10.1007/s00009-018-1226-5
Keywords
- Generalized Orlicz–Morrey spaces
- Lipschitz spaces
- fractional maximal operator
- Riesz potential
- Calderón–Zygmund operator
- commutator