Variable exponent weighted norm inequality for generalized Riesz potentials on the unit ball

• Autores: Fumi-Yuki Maeda, Yoshihiro Mizuta, Tetsu Shimomura
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 69, Fasc. 3, 2018, págs. 377-394
• Idioma: inglés
• DOI: 10.1007/s13348-017-0210-x
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• Resumen

  • Our aim in this paper is to establish variable exponent weighted norm inequalities for generalized Riesz potentials on the unit ball via norm inequalities in variable exponent non-homogeneous central Herz–Morrey spaces on the unit ball. As an application, we shall show Sobolev-type integral representation for a C^1-function on {\mathbb R}^N{\setminus } \{0\} which vanishes outside the unit ball.

• Referencias bibliográficas
  • Capone, C., Cruz-Uribe, D., Fiorenza, A.: The fractional maximal operator and fractional integrals on variable L^p spaces. Rev. Mat. Iberoamericana...
  • Cruz-Uribe, D., Fiorenza, A., Neugebauer, C.J.: The maximal function on variable L^p spaces. Ann. Acad. Sci. Fenn. Math. 28, 223–238 (2003)
  • Cruz-Uribe, D., Fiorenza, A., Neugebauer, C.J.: The maximal function on variable L^p spaces. Ann. Acad. Sci. Fenn. Math. 29, 247–249 (2004)
  • Diening, L., Harjulehto, P., Hästö, P., R\stackrel{\circ }{\rm u}žička, M.: Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes...
  • Futamura, T., Kishi, K., Mizuta, Y.: A generalization of Bôcher’s theorem for polyharmonic functions. Hiroshima Math. J. 31, 59–70 (2001)
  • Futamura, T., Kitaura, K., Mizuta, Y.: Riesz decomposition for superbiharmonic functions in the unit ball. Hokkaido Math. J. 38, 683–700 (2009)
  • Futamura, T., Mizuta, Y., Ohno, T.: Riesz decomposition for super-polyharmonic functions in the punctured unit ball. Stud. Sci. Math. Hungar....
  • Izuki, M., Nakai, E., Sawano, Y.: The Hardy-Littlewood maximal operator on Lebesgue spaces with variable exponent. RIMS Kokyuroku Bessatsu...
  • Izuki, M., Nakai, E., Sawano, Y.: Function spaces with variable exponents—an introduction. Sci. Math. Jpn. 77, 187–315 (2014)
  • Kurokawa, T.: A weighted norm inequality for potentials of order (m, k). J. Math. Kyoto Univ. 26–2, 203–211 (1986)
  • Mizuta, Y.: Potential Theory in Euclidean spaces. Gakkōtosho, Tokyo (1996)
  • Mizuta, Y.: Integral representations, differentiability properties and limits at infinity for Beppo Levi functions. Potential Anal. 6, 237–276...
  • Mizuta, Y., Shimomura, T.: Weighted Sobolev inequality in Musielak–Orlicz space. J. Math. Anal. Appl. 388, 86–97 (2012)
  • Mizuta, Y., Shimomura, T.: Weighted Morrey spaces of variable exponent and Riesz potentials. Math. Nachr. 288, 984–1002 (2015)
  • Muckenhoupt, B., Wheeden, R.L.: Weighted norm inequalities for fractional integrals. Trans. Am. Math. Soc. 192, 261–274 (1974)
  • Samko, N., Samko, S., Vakulov, B.: Weighted Sobolev theorem in Lebesgue spaces with variable exponent. J. Math. Anal. Appl. 335, 560–583 (2007)
  • Shimomura, T., Mizuta, Y.: Taylor expansion of Riesz potentials. Hiroshima Math. J. 25, 595–621 (1995)