Singular integral operators on Nakano spaces with weights having finite sets of discontinuities

Alexei Yu. Karlovich. "Singular integral operators on Nakano spaces with weights having finite sets of discontinuities." Banach Center Publications 92.1 (2011): 143-166. <http://eudml.org/doc/281604>.

@article{AlexeiYu2011,
abstract = {In 1968, Gohberg and Krupnik found a Fredholm criterion for singular integral operators of the form aP + bQ, where a,b are piecewise continuous functions and P,Q are complementary projections associated to the Cauchy singular integral operator, acting on Lebesgue spaces over Lyapunov curves. We extend this result to the case of Nakano spaces (also known as variable Lebesgue spaces) with certain weights having finite sets of discontinuities on arbitrary Carleson curves.},
author = {Alexei Yu. Karlovich},
journal = {Banach Center Publications},
keywords = {Cauchy singular integral operator; indices of submultiplicative functions; Carleson curve; one-sided invertibility; piecewise continuous function; weighted Nakano space; Lebesgue spaces with variable exponents},
language = {eng},
number = {1},
pages = {143-166},
title = {Singular integral operators on Nakano spaces with weights having finite sets of discontinuities},
url = {http://eudml.org/doc/281604},
volume = {92},
year = {2011},
}

TY - JOUR
AU - Alexei Yu. Karlovich
TI - Singular integral operators on Nakano spaces with weights having finite sets of discontinuities
JO - Banach Center Publications
PY - 2011
VL - 92
IS - 1
SP - 143
EP - 166
AB - In 1968, Gohberg and Krupnik found a Fredholm criterion for singular integral operators of the form aP + bQ, where a,b are piecewise continuous functions and P,Q are complementary projections associated to the Cauchy singular integral operator, acting on Lebesgue spaces over Lyapunov curves. We extend this result to the case of Nakano spaces (also known as variable Lebesgue spaces) with certain weights having finite sets of discontinuities on arbitrary Carleson curves.
LA - eng
KW - Cauchy singular integral operator; indices of submultiplicative functions; Carleson curve; one-sided invertibility; piecewise continuous function; weighted Nakano space; Lebesgue spaces with variable exponents
UR - http://eudml.org/doc/281604
ER -