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Abstract:

We prove a weighted version of the Hardy-Littlewood-Sobolev inequality for radially symmetric functions, and show that the range of admissible power weights appearing in the classical inequality due to Stein and Weiss can be improved in this particular case. © 2013 University of Illinois.

Registro:

Documento: Artículo
Título:On weighted inequalities for fractional integrals of radial functions
Autor:De Nápoli, P.L.; Drelichman, I.; Durán, R.G.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Año:2011
Volumen:55
Número:2
Página de inicio:575
Página de fin:587
Título revista:Illinois Journal of Mathematics
Título revista abreviado:Ill. J. Math.
ISSN:00192082
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00192082_v55_n2_p575_DeNapoli

Referencias:

  • Denápoli, P.L., Drelichman, I., Durán, R.G., Radial solutions for Hamiltonian elliptic systems with weights, Adv (2009) Nonlinear Stud, 9, pp. 579-593. , MR 2536956
  • Gasper, G., Stempak, K., Trebels, W., Fractional integration for Laguerre expansions, Mathods Appl (1995) Anal, 2, pp. 67-75. , MR 1337453
  • Grafakos, L., (2004) Classical and Modern Fourier Analysis, Pearson Education, , Inc., Upper Saddle River, NJ, MR 2449250
  • Hidano, K., Kurokawa, Y., Weighted HLS inequalities for radial functions and Strichartz estimates for Wave and Schr¨odinger equations (2008) Illinois J. Math, 52, pp. 365-388. , MR 2524642
  • Hardy, G.H., Littlewood, J.E., Some properties of fractional integrals, I (1928) Math. Z, 27, pp. 565-606. , MR 1544927
  • Lions, P.L., Sym´etrie et compacit´e dans les espaces de Sobolev (1982) J. Funct. Anal, 49, pp. 315-334. , MR 0683027
  • Rother, W., Some existence theorems for the equation −Δu + K(X)up = 0 (1990) Comm. Partial Differential Equations, 15, pp. 1461-1473. , MR 1077474
  • Sawyer, E., Wheeden, R.L., Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces (1992) Amer. J Math, 114, pp. 813-874. , MR 1175693
  • Stein, E.M., (1970) Singular Integrals and Differentiability Properties of Functions, , Princeton University Press, Princeton, MR
  • Stein, E.M., Weiss, G., Fractional integrals on n-dimensional Euclidean space (1958) J. Math. Mech, 7, pp. 503-514. , MR 0098285
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Citas:

---------- APA ----------
De Nápoli, P.L., Drelichman, I. & Durán, R.G. (2011) . On weighted inequalities for fractional integrals of radial functions. Illinois Journal of Mathematics, 55(2), 575-587.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00192082_v55_n2_p575_DeNapoli [ ]
---------- CHICAGO ----------
De Nápoli, P.L., Drelichman, I., Durán, R.G. "On weighted inequalities for fractional integrals of radial functions" . Illinois Journal of Mathematics 55, no. 2 (2011) : 575-587.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00192082_v55_n2_p575_DeNapoli [ ]
---------- MLA ----------
De Nápoli, P.L., Drelichman, I., Durán, R.G. "On weighted inequalities for fractional integrals of radial functions" . Illinois Journal of Mathematics, vol. 55, no. 2, 2011, pp. 575-587.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00192082_v55_n2_p575_DeNapoli [ ]
---------- VANCOUVER ----------
De Nápoli, P.L., Drelichman, I., Durán, R.G. On weighted inequalities for fractional integrals of radial functions. Ill. J. Math. 2011;55(2):575-587.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00192082_v55_n2_p575_DeNapoli [ ]