Hiroshima Mathematical Journal

Fractional integrals on Herz-Morrey spaces with variable exponent

Mitsuo Izuki

Full-text: Open access


Our aim in this paper is to prove the boundedness of fractional integrals from the Herz-Morrey space with variable exponent $M\dot{K}^{\alpha ,\lambda}_{q_1, p_1(\, \cdot \, )}(\R^n)$ to $M\dot{K}^{\alpha ,\lambda}_{q_2, p_2(\, \cdot \, )}(\R^n)$.

Article information

Hiroshima Math. J., Volume 40, Number 3 (2010), 343-355.

First available in Project Euclid: 8 December 2010

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B35: Function spaces arising in harmonic analysis 46B15: Summability and bases [See also 46A35]

Herz-Morrey space with variable exponent fractional integral


Izuki, Mitsuo. Fractional integrals on Herz-Morrey spaces with variable exponent. Hiroshima Math. J. 40 (2010), no. 3, 343--355. doi:10.32917/hmj/1291818849. https://projecteuclid.org/euclid.hmj/1291818849

Export citation


  • C. Capone, D. Cruz-Uribe, SFO and A. Fiorenza, The fractional maximal operator and fractional integrals on variable $L^p$ spaces, Rev. Mat. Iberoamericana 23 (2007), 743--770.
  • D. Cruz-Uribe, A. Fiorenza and C. J. Neugebauer, The maximal function on variable $L^p$ spaces, Ann. Acad. Sci. Fenn. Math. 28 (2003), 223--238, and 29 (2004), 247--249.
  • L. Diening, Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces $L^p(\, \cdot \, )$ and $W^k, p(\, \cdot \, )$, Math. Nachr. 268 (2004), 31--43.
  • L. Diening, Maximal functions on Musielak-Orlicz spaces and generalized Lebesgue spaces, Bull. Sci. Math. 129 (2005), 657--700.
  • M. Izuki, Herz and amalgam spaces with variable exponent, the Haar wavelets and greediness of the wavelet system, East J. Approx. 15 (2009), 87--109.
  • M. Izuki, Boundedness of vector-valued sublinear operators on Herz--Morrey spaces with variable exponent, Math. Sci. Res. J. 13 (2009), 243--253.
  • O. Kováčik and J. Rákosník, On spaces $L^p(x)$ and $W^k,p(x)$, Czechoslovak Math. 41 (116) (1991), 592--618.
  • S. Z. Lu and D. C. Yang, Hardy-Littlewood-Sobolev theorems of fractional integration on Herz-type spaces and its applications, Can. J. Math. 48 (1996), 363--380.
  • S. Lu and L. Xu, Boundedness of rough singular integral operators on the homogeneous Morrey-Herz spaces, Hokkaido Math. J. 34 (2005), 299--314.
  • A. Nekvinda, Hardy-Littlewood maximal operator on $L^p(x)(\R^n)$, Math. Inequal. Appl. 7 (2004), 255--265.