Geodesic
Singular Integral Operators on Weighted Variable Exponent Lebesgue Spaces on Composed Carleson Curves
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 87-92.

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

The paper is devoted to singular integral operators acting on weighted variable exponent Lebesgue spaces on certain composed Carleson curves. Necessary and sufficient conditions for Fredholmness and an index formula are obtained.
Keywords: singular integral operator
Mots-clés : variable exponent Lebesgue space. 
@article{FAA_2012_46_1_a10,
     author = {V. S. Rabinovich and S. G. Samko},
     title = {Singular {Integral} {Operators} on {Weighted} {Variable} {Exponent} {Lebesgue} {Spaces} on {Composed} {Carleson} {Curves}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {87--92},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a10/}
}
TY  - JOUR
AU  - V. S. Rabinovich
AU  - S. G. Samko
TI  - Singular Integral Operators on Weighted Variable Exponent Lebesgue Spaces on Composed Carleson Curves
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2012
SP  - 87
EP  - 92
VL  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a10/
LA  - ru
ID  - FAA_2012_46_1_a10
ER  - 
%0 Journal Article
%A V. S. Rabinovich
%A S. G. Samko
%T Singular Integral Operators on Weighted Variable Exponent Lebesgue Spaces on Composed Carleson Curves
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2012
%P 87-92
%V 46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a10/
%G ru
%F FAA_2012_46_1_a10
V. S. Rabinovich; S. G. Samko. Singular Integral Operators on Weighted Variable Exponent Lebesgue Spaces on Composed Carleson Curves. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 87-92. http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a10/

[1] A. Böttcher, Yu. I. Karlovich, Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators, Progress in Math., 154, Birkhauser, Basel, 1997 | DOI | MR | Zbl

[2] A. Böttcher, Yu. I. Karlovich, V. S. Rabinovich, J. Operator Theory, 43:1 (2000), 171–198 | MR | Zbl

[3] A. Böttcher, Yu. I. Karlovich, V. S. Rabinovich, Manuscripta Math., 95:3 (1998), 363–376 | DOI | MR | Zbl

[4] I. C. Gohberg, N. Ya. Krupnik, I. M. Spitkovsky, Integral Equations Operator Theory, 17:3 (1993), 322–327 | DOI | MR

[5] A. Yu. Karlovich, Operator Algebras, Operator Theory and Applications, Operator Theory Adv. Appl., 195, Birkhäuser, Basel, 2010, 185–212 | MR | Zbl

[6] A. Yu. Karlovich, Topics in Operator Theory 1: Operators, Matrices and Analytic Functions, Operator Theory Adv. Appl., 202, 2010, 321–336 | MR | Zbl

[7] A. Yu. Karlovich, arXiv: 1002.4813v1

[8] V. Kokilashvili, S. Samko, Proc. A. Razmadze Math. Inst., 131 (2003), 61–78 | MR | Zbl

[9] V. Kokilashvili, S. Samko, Proc. A. Razmadze Math. Inst., 138 (2005), 106–110 | MR | Zbl

[10] V. Kokilashvili, V. Paatashvili, S. Samko, Operator Theory Adv. Appl., 170, dedicated to 70th birthday of Prof. I. B. Simonenko, Birkhäuser, Basel, 2007, 167–186 | DOI | MR

[11] V. Kokilashvili, N. Samko, S. Samko, Math. Nachr., 280:9–10 (2007), 1145–1156 | DOI | MR | Zbl

[12] V. S. Rabinovich, Izv. RAN, ser. matem., 60:6 (1996), 169–200 | DOI | MR | Zbl

[13] V. Rabinovich, S. Samko, Integral Equations and Operator Theory, 60:4 (2008), 507–537, Birkhauser Verlag | DOI | MR

[14] I. B. Simonenko, Chin Ngok Min, Lokalnyi metod v teorii odnomernykh singulyarnykh integralnykh uravnenii s kusochno-nepreryvnymi koeffitsientami. Neterovost, Izd-vo Rostovskogo un-ta, 1986 | MR

[15] I. B. Simonenko, Izv. AN SSSR, ser. matem., 29:3 (1965), 567–586 | MR | Zbl

[16] I. M. Spitkovsky, J. Funct. Anal., 105:1 (1992), 129–143 | DOI | MR | Zbl