The Riemann-Hilbert problem in the class of Cauchy type integrals with densities of grand Lebesgue spaces

被引：3

作者：

Kokilashvili, Vakhtang ^{[1
,2
]}

Meskhi, Alexander ^{[1
,3
]}

Paatashvili, Vakhtang ^{[1
,3
]}

机构：

[1] I Javakhishvili Tbilisi State Univ, A Razmadze Math Inst, Dept Math Anal, 6 Tamarashvili St, GE-0177 Tbilisi, Georgia

[2] Int Black Sea Univ, 3 Agmashenebeli Ave, GE-0131 Tbilisi, Georgia

[3] Georgian Tech Univ, Dept Math, Fac Informat & Control Syst, 77 Kostava St, GE-0175 Tbilisi, Georgia

来源：

TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE | 2016年 / 170卷 / 02期

关键词：

Grand Lebesgue spaces; Riemann-Hilbert problem; Cauchy type integrals; Weights;

D O I：

10.1016/j.trmi.2016.07.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The present paper deals with a solution of the Riemann-Hilbert problem in the class of Cauchy type integrals with densities of certain new nonstandard Banach function spaces. The solvability conditions are explored and the solutions (if any) are constructed explicitly. (C) 2016 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V.

引用

页码：208 / 211

页数：4

共 10 条

[1] The maximal theorem for weighted grand Lebesgue spaces [J].

Fiorenza, Alberto ;

Gupta, Babita ;

Jain, Pankaj .

STUDIA MATHEMATICA, 2008, 188 (02) :123-133

[2] Inverting the p-harmonic operator [J].

Greco, L ;

Iwaniec, T ;

Sbordone, C .

MANUSCRIPTA MATHEMATICA, 1997, 92 (02) :249-258

[3] ON THE INTEGRABILITY OF THE JACOBIAN UNDER MINIMAL HYPOTHESES [J].

IWANIEC, T ;

SBORDONE, C .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1992, 119 (02) :129-143

[4]

Kokilashvili V., 2013, OPER THEORY ADV APPL, V229, P233

[5]

Kokilashvili V., 2016, VARIABLE EXPONENT H, VII, P577

[6]

Kokilashvili V., 2012, BOUNDARY VALUE PROBL

[7]

Kokilashvili V, 2014, BANACH CTR PUBLICATI, V102, P131

[8]

Kokilashvili V, 2009, GEORGIAN MATH J, V16, P547

[9]

Kokilshvili V., 2010, J MATH SCI-U TOKYO, V170, P20

[10]

Muskhelishvili N. I., 2008, SINGULAR INTEGRAL EQ

← 1 →