Erdelyi-Kober fractional Integrals on Hardy space and BMO

• Ho, Kwok-Pun ^[1]
  1. [1] Education University of Hong Kong

     Education University of Hong Kong

     RAE de Hong Kong (China)

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 3, 2020, págs. 663-677
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-03-0041
• Enlaces
  • Texto completo
• Resumen

  • The mapping properties of the multi. Erdélyi- Kober fractional integral operators on Hardy space and BMO. In particular, our main result gives the boundedness of the Erdélyi-Kober fractional integrals, the hypergeometric fractional integrals and the two-dimensional Weyl integrals on Hardy space and BMO.

• Referencias bibliográficas
  • A. Erdélyi, “On fractional integration and its application to the theory of hankel transforms”, The quarterly journal of mathematics, vol....
  • L. Grafakos, Modern fourier analysis, 2nd ed. New York, NY: Springer, 2009, doi: 10.1007/978-0-387-09434-2
  • K.-P. Ho, “Atomic decompositions of weighted Hardy-Morrey spaces”, Hokkaido mathematical journal, vol. 42, no. 1, pp. 131–157, Feb. 2013,...
  • K.-P. Ho, “Atomic decomposition of Hardy-Morrey spaces with variable exponents”, Annales academiæ scientiarum fennicæ mathematica, vol. 40,...
  • K.-P. Ho, “Atomic decompositions and Hardy’s inequality on weak Hardy-Morrey spaces”, Science China Mathematics, vol. 60, no. 3, pp. 449–468,...
  • K.-P. Ho, “Atomic decompositions of weighted Hardy spaces with variable exponents”, Tohoku mathematical journal, vol. 69, no. 3, pp. 383–413,...
  • K.-P. Ho, “Sublinear operators on weighted Hardy spaces with variable exponents”, Forum mathematicum, vol. 31, no. 3, pp. 607–617, May 2019,...
  • K.-P. Ho, “Integral operators on BMO and Campanato spaces”, Indagationes mathematicae, vol. 30, no. 6, pp. 1023–1035, Nov. 2019., doi: 10.1016/j.indag.2019.05.007
  • K.-P. Ho, “Sublinear operators on mixed-norm Hardy spaces with variable exponents”, Atti della Accademia Nazionale dei Lincei, Classe di Scienze...
  • K.-P. Ho, “Erdélyi-Kober fractional integral operators on ball Banach function spaces”, Rendiconti del Seminario matematico della Universita?...
  • K.-P. Ho, “Calderón-Zygmund operators, Bochner-Riesz means and Parametric Marcinkiewicz integrals on Hardy-Morrey spaces with variable exponents”,...
  • H. Jia and H. Wang, “Decomposition of Hardy–Morrey spaces”, Journal of mathematical analysis and applications, vol. 354, no. 1, pp. 99–110,...
  • V. Kiryakova, Generalized fractional calculus and applications. Harlow: Longman Scientific & Technical, 1994.
  • H. Kober, “On fractional integrals and derivatives”, The quarterly journal of mathematics, vol. os-11, no. 1, pp. 193–211, Jan. 1940, doi:...
  • E. R. Love, “Some integral equations involving hypergeometric functions”, Proceedings of the Edinburgh Mathematical Society, vol. 15, no....
  • S. Lu and D. Yang, “The local versions of ?p(?n) spaces at the origin”, Studia mathematica, vol. 116, no. 2, pp. 103-131, 1995. [On line]....
  • S. Lu, D. Ang, and G. Hu, Herz type spaces and their applications. Beijing: China Press, 2008.
  • A. M. Mathai and R. K. Saxena, Generalized hypergeometric functions with applications in statistics and physical sciences, vol. 348. Berlin:...
  • E. Nakai and Y. Sawano, “Hardy spaces with variable exponents and generalized Campanato spaces”, Journal of functional analysis, vol. 262,...
  • G. Pagnini, “Erdélyi-Kober fractional diffusion”, Fractional calculus and applied analysis, vol. 15, no. 1, Mar. 2012, doi: 10.2478/s13540-012-0008-1
  • ?. P?ociniczak, “Approximation of the Erdélyi--Kober operator with application to the time-fractional Porous medium equation”, SIAM journal...
  • ?. P?ociniczak and M. ?wita?a, “Existence and uniqueness results for a time-fractional nonlinear diffusion equation”, Journal of mathematical...
  • ?. P?ociniczak, “Numerical method for the time-fractional porous medium equation”, SIAM journal on numerical analysis, vol. 57, no. 2, pp....
  • Y. Sawano, K.-P. Ho, D. Yang, and S. Yang, “Hardy spaces for ball quasi-Banach function spaces”, Dissertationes mathematicae, vol. 525, pp....
  • I. A. Sneddon, “The use in mathematical physics of Erdlyi-Kober operators and of some of their generalizations”, in Fractional calculus and...
  • E. M. Stein, Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals. Princeton, NJ: Princeton University Press,...