A note on convolution operators on Riesz Bounded variation spaces

• Gutierrez, Lucía ^[1] ; Guzmán, Oscar M. ^[2]
  1. [1] Universidad Militar Nueva Granada

     Universidad Militar Nueva Granada

     Colombia

     
  2. [2] Universidad ECCI.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 6, 2021, págs. 1603-1613
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4357
• Enlaces
  • Texto completo
• Resumen

  • We show some estimates and approximation results of operators of convolution type defined on Riesz Bounded variation spaces in Rn . We also state some embedding results that involve the collection of generalized absolutely continuous functions

• Referencias bibliográficas
  • C. Jordan, “Sur la series de Fourier”, Comptes Rendus de l’Académie des Sciences Paris, vol. 92, pp. 228-230, 1881.
  • F. Riesz, “Untersuchungen uber systeme integrierbarer funktrionen”, Mathematische annales, vol. 69, no. 4, pp. 449-497, 1910.
  • J. Appell, J. Banas, and N. Merentes, Bounded variation and around. Berlin: De Gruyter, 2014
  • L. Tonelli, “Su alcuni concetti dellánalisi moderna”, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, vol. 11, no. 1-2,...
  • L. Young, “Sur une généralisation de la notion de variation de puissance p-ieme bornee au sens de M. Wiener, et sur la convergence des séries...
  • B. Lenze, “On constructive one-sided approximation of multivariate functions of bounded variation”, Numerical functional analysis and optimization,...
  • S. Barza and M. Lind, “A new variational characterization of Sobolev spaces”, The journal of geometric analysis, vol. 25, no. 4, pp. 2185-2195,...
  • L. Angeoloni, “A new concept of multidimensional variation in the sense of Riesz and applications to integral operators”, Mediterranean journal...
  • L. Angeloni and G. Vinti, “A review on approximation results for integral operators in the space of functions of bounded variation”, Journal...
  • C. Bardaro, J. Musielak, and G. Vinti, Nonlinear integral operators and applications. Berlin: De Gruyter, 2003.
  • P. Butzer and S. Jansche, “A direct approach to the Mellin transform”, Journal of Fourier analysis and applications, vol. 3, no. 4, pp. 325-376,...
  • L. Angeloni and G. Vinti, “Convergence andd rate of approximation for linear integral operators in BVϕ-spaces in multidimensional settins”,...
  • J. Maly, “Absolutely continuous functions of several variables”, Journal of mathematical analysis and applications, vol. 231, no. 2, pp. 492-508,...
  • H. Brezis, Functional analysis, Sobolev spaces and partial differential equations. New York, NY: Springer, 2011.
  • J. Heinonen, “Lectures on Lipschitz analysis”, University of Jyväskylä, Department of Mathematics and Statistics, Finland, Rep., 100, 2005.