Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz–Morrey spaces of the third kind
Tóm tắt
In the present paper, we will characterize the boundedness of the generalized fractional integral operators
$$I_{\rho }$$
and the generalized fractional maximal operators
$$M_{\rho }$$
on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators
$$M_{\rho }$$
and
$$I_{\rho }$$
on generalized Orlicz–Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators
$$M_{\rho }$$
and
$$I_{\rho }$$
on generalized Orlicz–Morrey spaces.
Tài liệu tham khảo
Adams, D.R.: A note on Riesz potentials. Duke Math. J. 42, 765–778 (1975)
Cianchi, A.: Strong and weak type inequalities for some classical operators in Orlicz spaces. J. Lond. Math. Soc. 60(1), 187–202 (1999)
Deringoz, F., Guliyev, V.S., Samko, S.: Boundedness of maximal and singular operators on generalized Orlicz–Morrey spaces. Oper. Theory Oper. Algebras Appl. Ser. Oper. Theory: Adv. Appl. 242, 139–158 (2014)
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 Transform. Spec. Funct. 28(4), 284–299 (2017)
Deringoz, F., Guliyev, V.S., Hasanov, S.G.: Characterizations for the Riesz potential and its commutators on generalized Orlicz–Morrey spaces. J. Inequal. Appl. (2016). https://doi.org/10.1186/s13660-016-1192-z
Eridani, A., Gunawan, H., Nakai, E., Sawano, Y.: Characterizations for the generalized fractional integral operators on Morrey spaces. Math. Inequal. Appl. 17(2), 761–777 (2014)
Gala, S., Sawano, Y., Tanaka, H.: A remark on two generalized Orlicz–Morrey spaces. J. Approx. Theory 198, 1–9 (2015)
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)
Guliyev, V.S., Ismayilova, A.F., Kucukaslan, A., Serbetci, A.: Generalized Fractional integral operators on generalized local Morrey spaces. J. Funct. Spaces (2015). https://doi.org/10.1155/2015/594323
Hakim, D.I., Nakai, E., Sawano, Y.: Generalized fractional maximal operators and vector-valued inequalities on generalized Orlicz–Morrey spaces. Rev. Mat. Complut. 29(1), 59–90 (2016)
Hästo, P.A.: The maximal operator on generalized Orlicz spaces. J. Funct. Anal. 269(12), 4038–4048 (2015)
Hedberg, L.I.: On certain convolution inequalities. Proc. Am. Math. Soc. 36, 505–510 (1972)
Kawasumi R., Nakai E.: Pointwise multipliers on weak Orlicz spaces. arXiv:1811.02858
Kokilashvili, V., Krbec, M.M.: Weighted Inequalities in Lorentz and Orlicz Spaces. World Scientific, Singapore (1991)
Maligranda, L.: Orlicz spaces and interpolation, Seminários de Matemática, vol. 5 (1989)
Mizuta, Y., Nakai, E., Ohno, T., Shimomura, T.: Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials. J. Math. Soc. Jpn. 62(3), 707–744 (2010)
Nakai, E.: A characterization of pointwise multipliers on the Morrey spaces. Sci. Math. 3(3), 445–454 (2000)
Nakai, E.: On generalized fractional integrals in the Orlicz spaces. In: Proceedings of the Second ISAAC Congress, Vol. 1, pp. 75–81. (Fukuoka, 1999), Int. Soc. Anal. Appl. Comput., 7, Kluwer Acad. Publ., Dordrecht (2000)
Nakai, E.: On generalized fractional integrals. Taiwan. J. Math. 5, 587–602 (2001)
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 2002, pp. 389–401 (2000)
Nakai, E.: Generalized fractional integrals on Orlicz–Morrey spaces. In: Banach and Function Spaces, pp. 323–333. (Kitakyushu, 2003), Yokohama Publishers, Yokohama (2004)
Nakai, E., Sumitomo, H.: On generalized Riesz potentials and spaces of some smooth functions. Sci. Math. Jpn. 54(3), 463–472 (2001)
O’Neil, R.: Fractional integration in Orlicz spaces. I. Trans. Am. Math. Soc. 115, 300–328 (1965)
Pustylnik, E.: Generalized potential type operators on rearrangement invariant spaces. Israel Math. Conf. Proc. 13(3), 161–171 (1999)
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. Dekker, New York (1991)
Spanne, S.: Some function spaces defined using the mean oscillation over cubes. Ann. Scuola Norm. Sup. Pisa 19(3), 593–608 (1965)
Sawano, Y.: Theory of Besov spaces, Development in Mathematics vol. 56
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)
Weiss, G.: A note on Orlicz spaces. Portugal Math. 15, 35–47 (1950)