Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class A∞. The main tool is a discretization in terms of an almost orthogonal wavelet expansion adapted to the radial situation. © 2016 Instytut Matematyczny PAN.

Registro:

Documento: Artículo
Título:Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces
Autor:De Nápoli, P.L.; Drelichman, I.; Saintier, N.
Filiación:IMAS (UBA-CONICET) and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria, Buenos Aires, 1428, Argentina
Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria, Buenos Aires, 1428, Argentina
Palabras clave:Embedding theorems; Muckenhoupt weights; Radial functions; Wavelet bases
Año:2016
Volumen:233
Número:1
Página de inicio:47
Página de fin:65
DOI: http://dx.doi.org/10.4064/sm8383-4-2016
Título revista:Studia Mathematica
Título revista abreviado:Stud. Math.
ISSN:00393223
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v233_n1_p47_DeNapoli

Referencias:

  • Andersen, K.F., John, R.T., Weighted inequalities for vector-valued maximal functions and singular integrals (1980) Studia Math, 69, pp. 19-31
  • Bui, H.-Q., Weighted besov and triebel lizorkin spaces: Interpolation by the real method (1982) Hiroshima Math. J, 12, pp. 581-605
  • Bui, H.-Q., Paluszynski, M., Taibleson, M.R., A maximal characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces (1996) Studia Math, 119, pp. 219-246
  • Cui, L., Peng, L., Biorthogonal radial multiresolution in dimension three (2009) J. Comput. Appl. Math, 224, pp. 581-591
  • De Nápoli, P.L., Drelichman, I., (2014) Elementary Proofs of Embedding Theorems for Potential Spaces of Radial Functions, , arXiv 1404 7468
  • De Nápoli, P.L., Drelichman, I., Weighted convolution inequalities for radial functions (2015) Ann. Mat. Pura Appl, 194, pp. 167-181
  • De Nápoli, P.L., Drelichman, I., Durán, R.G., Radial solutions for Hamiltonian elliptic systems with weights (2009) Adv Nonlinear Stud, 9, pp. 579-593
  • Duoandikoetxea, J., Moyua, A., Oruetxebarria, O., Seijo, E., Radial Ap weights with applications to the disc multiplier and the Bochner-Riesz operators (2008) Indiana Univ. Math. J, 57, pp. 1261-1281
  • Epperson, J., Frazier, M., An almost orthogonal radial wavelet expansion for radial distributions (1995) J. Fourier Anal. Appl, 1, pp. 311-353
  • Franke, J., On the spaces fs p;q of triebel-lizorkin type: Pointwise multipliers and spaces on domains (1986) Math. Nachr, 125, pp. 29-68
  • García-Cuerva, J., De Rubio Francia, J.L., (1985) Weighted Norm Inequalities and Related Topics, , North-Holland, Amsterdam
  • Haroske, D., Skrzypczak, L., Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights (2008) I , Rev. Mat. Complut, 21, pp. 135-177
  • Haroske, D., Skrzypczak, L., Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. General weights (2011) Ann. Acad. Sci. Fenn. Math, 36, pp. 111-138
  • Haroske, D., Skrzypczak, L., Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases (2011) J. Funct. Spaces Appl, 9, pp. 129-178
  • Jawerth, B., Some observations on besov and lizorkin-Triebel spaces (1977) Math. Scand, 40, pp. 94-104
  • Kokilashvili, V.M., Maximal inequalities and multipliers in weighted Lizorkin-Triebel spaces (1978) Soviet Math. Dokl, 19, pp. 271-276
  • Köhn, T., Entropy numbers in weighted function spaces. The case of intermediate weights (2006) Proc. Steklov Inst. Math, 255, pp. 159-168
  • Köhn, T., Leopold, H.-G., Sickel, W., Skrzypczak, L., Entropy numbers of embeddings of weighted Besov spaces (2006) Constr. Approx, 23, pp. 61-77
  • Köhn, T., Leopold, H.-G., Sickel, W., Skrzypczak, L., Entropy numbers of embeddings of weighted Besov spaces. II (2006) Proc. Edinburgh Math. Soc, 2 (49), pp. 331-359
  • Köhn, T., Leopold, H.-G., Sickel, W., Skrzypczak, L., Entropy numbers of embeddings of weighted Besov spaces. III. Weights of logarithmic type (2007) Math. Z, 255, pp. 1-15
  • Köhn, T., Leopold, H.-G., Sickel, W., Skrzypczak, L., Entropy numbers of Sobolev embeddings of radial Besov spaces (2003) J. Approx. Theory, 121, pp. 244-268
  • Lions, P.-L., Symétrie et compacité dans les espaces de Sobolev (1982) J. Funct. Anal, 49, pp. 315-334
  • Meyries, M., Veraar, M., Sharp embedding results for spaces of smooth functions with power weights (2012) Studia Math, 208, pp. 257-293
  • Meyries, M., Veraar, M., Characterization of a class of embeddings for function spaces with Muckenhoupt weights (2014) Arch. Math. (Basel, 103, pp. 435-449
  • Ni, W.M., A nonlinear Dirichlet problem on the unit ball and its applications (1982) Indiana Univ. Math. J, 31, pp. 801-807
  • Peetre, J., New thoughts on besov spaces (1976) Duke Univ. Math. Ser, 1. , Math. Dep. Duke Univ., Durham, NC
  • Peetre, J., On spaces of Triebel-Lizorkin type (1975) Ark. Mat, 13, pp. 123-130
  • Rauhut, H., Rösler, M., Radial multiresolution in dimension three (2005) Constr. Approx, 22, pp. 193-218
  • Rychkov, V.S., Littlewood-Paley theory and function spaces with Aloc p weights (2001) Math. Nachr, 224, pp. 145-180
  • Sickel, W., Skrzypczak, L., Radial subspaces of besov and lizorkin-Triebel classes: Extended strauss lemma and compactness of embeddings (2000) J. Fourier Anal. Appl, 6, pp. 639-662
  • Sickel, W., Skrzypczak, L., On the interplay of regularity and decay in case of radial functions II. Homogeneous spaces (2012) J. Fourier Anal. Appl, 18, pp. 548-582
  • Sickel, W., Skrzypczak, L., Vybirál, J., On the interplay of regularity and decay in case of radial functions I. Inhomogeneous spaces (2012) Comm. Contemp. Math, 14 (1), p. 60. , 1250005
  • Strauss, W.A., Existence of solitary waves in higher dimensions (1977) Comm. Math. Phys, 55, pp. 149-162
  • Triebel, H., (1983) Theory of Function Spaces, , Geest & Portig, Leipzig
  • Triebel, H., (2006) Theory of Function Spaces III , Monogr. Math, 100. , Birkhäuser, Basel

Citas:

---------- APA ----------
De Nápoli, P.L., Drelichman, I. & Saintier, N. (2016) . Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces. Studia Mathematica, 233(1), 47-65.
http://dx.doi.org/10.4064/sm8383-4-2016
---------- CHICAGO ----------
De Nápoli, P.L., Drelichman, I., Saintier, N. "Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces" . Studia Mathematica 233, no. 1 (2016) : 47-65.
http://dx.doi.org/10.4064/sm8383-4-2016
---------- MLA ----------
De Nápoli, P.L., Drelichman, I., Saintier, N. "Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces" . Studia Mathematica, vol. 233, no. 1, 2016, pp. 47-65.
http://dx.doi.org/10.4064/sm8383-4-2016
---------- VANCOUVER ----------
De Nápoli, P.L., Drelichman, I., Saintier, N. Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces. Stud. Math. 2016;233(1):47-65.
http://dx.doi.org/10.4064/sm8383-4-2016