TY - JOUR
T1 - The cauchy singular integral operator on weighted variable lebesgue spaces
AU - Karlovich, Alexei Yu
AU - Spitkovsky, Ilya M.
N1 - Publisher Copyright:
© 2014 Springer Basel.
PY - 2014
Y1 - 2014
N2 - Let p : ℝ → (1,∞) be a globally log-Hölder continuous variable exponent and w : ℝ → [0,∞] be a weight. We prove that the Cauchy singular integral operator S is bounded on the weighted variable Lebesgue space Lp(⋅)(ℝ,w) = {f : fw ∈ Lp(⋅)(ℝ)} if and only if the weight w satisfies (Formula Presented).
AB - Let p : ℝ → (1,∞) be a globally log-Hölder continuous variable exponent and w : ℝ → [0,∞] be a weight. We prove that the Cauchy singular integral operator S is bounded on the weighted variable Lebesgue space Lp(⋅)(ℝ,w) = {f : fw ∈ Lp(⋅)(ℝ)} if and only if the weight w satisfies (Formula Presented).
KW - Cauchy singular integral operator
KW - Hardy-littlewood maximal operator
KW - Log-Hölder continuous variable exponent
KW - Weighted variable lebesgue space
UR - http://www.scopus.com/inward/record.url?scp=84946071429&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84946071429&partnerID=8YFLogxK
U2 - 10.1007/978-3-0348-0648-0_17
DO - 10.1007/978-3-0348-0648-0_17
M3 - Article
AN - SCOPUS:84946071429
SN - 0255-0156
VL - 236
SP - 275
EP - 291
JO - Operator Theory: Advances and Applications
JF - Operator Theory: Advances and Applications
ER -