The Cone of Rearrangements for Generalized Bessel Potentials
Informatics and Automation, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 151-163.

Voir la notice de l'article provenant de la source Math-Net.Ru

A space of generalized Bessel potentials constructed on the basis of rearrangement-invariant spaces is considered. An equivalent description of the cone of decreasing rearrangements is proposed for functions from the space of generalized Bessel potentials. An additional characterization of the cone of decreasing rearrangements is obtained in the case of spaces separated from the space $L_1$.
@article{TRSPY_2008_260_a9,
     author = {M. L. Gol'dman},
     title = {The {Cone} of {Rearrangements} for {Generalized} {Bessel} {Potentials}},
     journal = {Informatics and Automation},
     pages = {151--163},
     publisher = {mathdoc},
     volume = {260},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a9/}
}
TY  - JOUR
AU  - M. L. Gol'dman
TI  - The Cone of Rearrangements for Generalized Bessel Potentials
JO  - Informatics and Automation
PY  - 2008
SP  - 151
EP  - 163
VL  - 260
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a9/
LA  - ru
ID  - TRSPY_2008_260_a9
ER  - 
%0 Journal Article
%A M. L. Gol'dman
%T The Cone of Rearrangements for Generalized Bessel Potentials
%J Informatics and Automation
%D 2008
%P 151-163
%V 260
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a9/
%G ru
%F TRSPY_2008_260_a9
M. L. Gol'dman. The Cone of Rearrangements for Generalized Bessel Potentials. Informatics and Automation, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 151-163. http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a9/

[1] Analiz – 3, Itogi nauki i tekhniki. Sovr. probl. matematiki. Fund. napr., 26, VINITI, M., 1988

[2] Mazya V. G., Prostranstva S. L. Soboleva, Izd-vo LGU, L., 1985 | MR

[3] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR

[4] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR

[5] Bennett C., Sharpley R., Interpolation of operators, Pure and Appl. Math., 129, Acad. Press, New York, 1988 | MR | Zbl

[6] Cianchi A., “A sharp embedding theorem for Orlicz–Sobolev spaces”, Indiana Univ. Math. J., 45:1 (1996), 39–65 | DOI | MR | Zbl

[7] Cianchi A., Pick L., “Sobolev embeddings into BMO, VMO and $L_\infty$”, Ark. Mat., 36:2 (1998), 317–340 | DOI | MR | Zbl

[8] Cwikel M., Pustylnik E., “Sobolev type embeddings in the limiting case”, J. Fourier Anal. and Appl., 4:4 (1998), 433–446 | DOI | MR | Zbl

[9] Pustylnik E. I., “Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz–Sobolev embeddings”, J. Funct. Spaces and Appl., 3:2 (2005), 183–208 | MR | Zbl

[10] Edmunds D., Kerman R., Pick L., “Optimal Sobolev imbeddings, involving rearrangement-invariant quasinorms”, J. Funct. Anal., 170:2 (2000), 307–355 | DOI | MR | Zbl

[11] Gogatishvili A., Neves J. S., Opic B., “Optimality of embeddings of Bessel-potential-type spaces”, Function spaces, differential operators and nonlinear analysis, Proc. Conf., Milovy, Czech Republ., May 28–June 2, 2004, Math. Inst. Acad. Sci. Czech Republ., Prague, 2005, 97–102

[12] Netrusov Yu. V., “Teoremy vlozheniya prostranstv Besova v idealnye prostranstva”, Zap. nauch. sem. LOMI, 159, Nauka, L., 1987, 69–82 | Zbl

[13] Netrusov Yu. V., “Teoremy vlozheniya prostranstv Lizorkina–Tribelya”, Zap. nauch. sem. LOMI, 159, Nauka, L., 1987, 103–112 | Zbl

[14] O'Neil R., “Convolution operators and $L(p,q)$ spaces”, Duke Math. J., 30 (1963), 129–142 | DOI | MR

[15] Kolyada V. I., “Rearrangements of functions and embedding of anisotropic spaces of Sobolev type”, East J. Approx., 4:2 (1998), 111–199 | MR | Zbl

[16] Kalyabin G. A., “Kharakterizatsiya prostranstv tipa Besova–Lizorkina–Tribelya s pomoschyu obobschennykh raznostei”, Tr. MIAN, 181, Nauka, M., 1988, 95–116 | MR

[17] Kalyabin G. A., Lizorkin P. I., “Spaces of functions of generalized smoothness”, Math. Nachr., 133 (1987), 7–32 | DOI | MR | Zbl

[18] Farkas W., Leopold H.-G., “Characterisations of function spaces of generalised smoothness”, Ann. Mat. Pura ed Appl., 185:1 (2006), 1–62 | DOI | MR | Zbl

[19] Haroske D., Limiting embeddings, entropy numbers and envelopes in function spaces, Habilitationsschrift, Univ. Jena, Jena, 2002

[20] Haroske D., Moura S., “Continuity envelopes of spaces of generalised smoothness, entropy and approximation numbers”, J. Approx. Theory, 128:2 (2004), 151–174 | DOI | MR | Zbl

[21] Goldman M. L., “O perestanovochno invariantnoi obolochke obobschennykh prostranstv Soboleva”, DAN, 405:1 (2005), 13–17 | MR

[22] Goldman M. L., “Rearrangement invariant envelopes of generalized Besov, Sobolev, and Calderon spaces”, The interaction of analysis and geometry, Contemp. Math., 424, Amer. Math. Soc., Providence, RI, 2007, 53–81 | MR | Zbl

[23] Goldman M. L., “Integralnye svoistva obobschennykh besselevykh potentsialov”, DAN, 414:2 (2007), 159–164 | MR

[24] Carro M. J., Raposo J. A., Soria J., Recent developments in the theory of Lorentz spaces and weighted inequalities, Mem. AMS, 187, No 877, Amer. Math. Soc., Providence, RI, 2007 ; arXiv: /math/0010010 | MR