Commutators of integral operators with functions in Campanato spaces on Orlicz-Morrey spaces
Tóm tắt
Từ khóa
Tài liệu tham khảo
Arai, R., Nakai, E.: Commutators of Calderón-Zygmund and generalized fractional integral operators on generalized Morrey spaces. Rev. Mat. Complut. 31(2), 287–331 (2018)
Coifman, R.R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variables. Ann. Math. (2) 103(3), 611–635 (1976)
Deringoz, F., Guliyev, V.S., Nakai, E., Sawano, Y., Shi, M.: Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz-Morrey spaces of the third kind. Positivity 23, 727–757 (2019)
Deringoz, F., Guliyev, V.S., Samko, S.: Boundedness of the maximal and singular operators on generalized Orlicz-Morrey spaces. Oper. Theory Adv. Appl. 242, 139–158 (2014). (Birkhäuser/Springer, Basel)
Di Fazio, G., Ragusa, M.A.: Commutators and Morrey spaces. Boll. Un. Mat. Ital. A (7) 5(3), 323–332 (1991)
Ding, Y., Yang, D., Zhou, Z.: Boundedness of sublinear operators and commutators on $$L^{p,\omega }({{\mathbb{R}}}^n)$$. Yokohama Math. J. 46(1), 15–27 (1998)
Fu, X., Yang, D., Yuan, W.: Boundedness of multilinear commutators of Calderón-Zygmund operators on Orlicz spaces over non-homogeneus spaces. Taiwanese J. Math. 16(6), 2203–2238 (2012)
Fu, X., Yang, D., Yuan, W.: Generalized fractional integrals and their commutators over non-homogeneous metric measure spaces. Taiwanese J. Math. 18(2), 509–557 (2014)
Guliyev, V.S., Deringoz, F., Hasanov, S.G.: Riesz potential and its commutators on Orlicz spaces. J. Inequal. Appl. 75, 18 (2017)
Guliyev, V.S., Hasanov, S.G., Sawano, Y., Noi, T.: Non-smooth atomic decompositions for generalized Orlicz-Morrey spaces of the third kind. Acta Appl. Math. 145, 133–174 (2016)
Iida, T.: Weighted estimates of higher order commutators generated by BMO-functions and the fractional integral operator on Morrey spaces. J. Inequal. Appl. 4, 23 (2016)
Janson, S.: Mean oscillation and commutators of singular integral operators. Ark. Mat. 16(2), 263–270 (1978)
Kita, H.: Orlicz Spaces and Their Applications (Japanese). Iwanami Shoten Publishers, Tokyo (2009)
Kokilashvili, V., Krbec, M.: Weighted Inequalities in Lorentz and Orlicz Spaces. World Scientific Publishing Co. Inc, River Edge (1991)
Komori-Furuya, Y.: Local good-$$\lambda $$ estimate for the sharp maximal function and weighted Morrey space. J. Funct. Spaces 651825, 4 (2015)
Komori, Y., Mizuhara, T.: Notes on commutators and Morrey spaces. Hokkaido Math. J. 32(2), 345–353 (2003)
Krasnoselsky, M.A., Rutitsky, Y.B.: Convex functions and Orlicz spaces. Translated from the first Russian edition by Leo F. Boron. P. Noordhoff Ltd., Groningen (1961)
Maligranda, L.: Orlicz spaces and interpolation, Seminars in mathematics 5, Departamento de Matemática, Universidade Estadual de Campinas, Brasil (1989)
Mizuhara, T.: Relations between Morrey and Campanato spaces with some growth functions, II. In: Proceedings of harmonic analysis seminar, vol. 11, pp. 67–74 (in Japanese) (1995)
Mizuhara, T.: Commutators of singular integral operators on Morrey spaces with general growth functions. Harmonic analysis and nonlinear partial differential equations (Kyoto, 1998). Sûrikaisekikenkyûsho Kôkyûroku 1102, 49–63 (1999)
Nakai, E.: On generalized fractional integrals in the Orlicz spaces. In: Proceedings of the Second ISAAC Congress, Vol. 1 (Fukuoka, 1999), Int. Soc. Anal. Appl. Comput., 7, Kluwer Acad. Publ., Dordrecht, pp. 75–81 (2000)
Nakai, E.: On generalized fractional integrals in the Orlicz spaces on spaces of homogeneous type. Sci. Math. Jpn. 54, 473–487 (2001)
Nakai, E.: On generalized fractional integrals on the weak Orlicz spaces, $${\rm BMO}_{\phi }$$, the Morrey spaces and the Campanato spaces, Function spaces, interpolation theory and related topics (Lund, 2000), de Gruyter, Berlin, pp. 389–401 (2002)
Nakai, E.: Generalized Fractional Integrals on Orlicz-Morrey Spaces, Banach and Function Spaces (Kitakyushu, 2003), pp. 323–333. Yokohama Publishers, Yokohama (2004)
Nakai, E.: The Campanato, Morrey and Hölder spaces on spaces of homogeneous type. Stud. Math. 176(1), 1–19 (2006)
Nakai, E.: Orlicz-Morrey spaces and the Hardy-Littlewood maximal function. Stud. Math. 188(3), 193–221 (2008)
Nakai, E.: Calderón-Zygmund Operators on Orlicz-Morrey Spaces and Modular Inequalities. Banach and Function Spaces II, pp. 393–410. Yokohama Publishers, Yokohama (2008)
Nakai, E.: A generalization of Hardy spaces $$H^p$$ by using atoms. Acta Math. Sin. (Engl. Ser.) 24(8), 1243–1268 (2008)
Nakai, E., Sumitomo, H.: On generalized Riesz potentials and spaces of some smooth functions. Sci. Math. Jpn. 54(3), 463–472 (2001)
Nakamura, S., Sawano, Y.: The singular integral operator and its commutator on weighted Morrey spaces. Collect. Math. 68(2), 145–174 (2017)
Orlicz, W.: Über eine gewisse Klasse von Räumen vom Typus B. Bull. Acad. Polonaise A 1932, 207–220 (1932). (reprinted in his Collected Papers, PWN, Warszawa 1988, 217–230)
Orlicz, W.: Über Räume $$(L^M)$$. Bull. Acad. Polonaise A 1936, 93–107 (1936). (reprinted in his Collected Papers, PWN, Warszawa 1988, 345–359)
Pérez, C.: Two weighted inequalities for potential and fractional type maximal operators. Indiana Univ. Math. J. 43, 663–683 (1994)
Rao, M.M., Ren, Z.D.: Theory of Orlicz Spaces. Marcel Dekker Inc., New York, Basel, Hong Kong (1991)
Sawano, Y., Sugano, S., Tanaka, H.: Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces. Trans. Am. Math. Soc. 363(12), 6481–6503 (2011)
Sawano, Y., Sugano, S., Tanaka, H.: Orlicz-Morrey spaces and fractional operators. Potential Anal. 36(4), 517–556 (2012)
Shi, M., Arai, R., Nakai, E.: Generalized fractional integral operators and their commutators with functions in generalized Campanato spaces on Orlicz spaces. Taiwanese J. Math. 23(6), 1339–1364 (2019)
Shirai, S.: Notes on commutators of fractional integral operators on generalized Morrey spaces. Sci. Math. Jpn. 63(2), 241–246 (2006)
Shirai, S.: Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on classical Morrey spaces. Hokkaido Math. J. 35(3), 683–696 (2006)
Tao, J., Yang, Da, Yang, Do: Boundedness and compactness characterizations of Cauchy integral commutators on Morrey spaces. Math. Methods Appl. Sci. 42(5), 1631–1651 (2019)
Tao, J., Yang, Da., Yang, Do.: Beurling-Ahlfors commutators on weighted Morrey spaces and applications to Beltrami equations. Potential Anal. (2020) (online first article). https://doi.org/10.1007/s11118-019-09814-7
Tsutsui, Y.: Sharp maximal inequalities and its application to some bilinear estimates. J. Fourier Anal. Appl. 17, 265–289 (2011)