TY - GEN
T1 - Singular integral operators on variable lebesgue spaces with radial oscillating weights
AU - Karlovich, Alexei Yu
PY - 2010/1/1
Y1 - 2010/1/1
N2 - We prove a Fredholm criterion for operators in the Banach algebra of singular integral operators with matrix piecewise continuous coefficients acting on a variable Lebesgue space with a radial oscillating weight over a logarithmic Carleson curve. The local spectra of these operators are massive and have a shape of spiralic horns depending on the value of the variable exponent, the spirality indices of the curve, and the Matuszewska-Orlicz indices of the weight at each point. These results extend (partially) the results of A. Böttcher, Yu. Karlovich, and V. Rabinovich for standard Lebesgue spaces to the case of variable Lebesgue spaces.
AB - We prove a Fredholm criterion for operators in the Banach algebra of singular integral operators with matrix piecewise continuous coefficients acting on a variable Lebesgue space with a radial oscillating weight over a logarithmic Carleson curve. The local spectra of these operators are massive and have a shape of spiralic horns depending on the value of the variable exponent, the spirality indices of the curve, and the Matuszewska-Orlicz indices of the weight at each point. These results extend (partially) the results of A. Böttcher, Yu. Karlovich, and V. Rabinovich for standard Lebesgue spaces to the case of variable Lebesgue spaces.
KW - Carleson curve
KW - Matuszewska-Orlicz indices
KW - Radial oscillating weight
KW - Submultiplicative function
KW - Variable exponent
KW - Variable Lebesgue space
UR - http://www.scopus.com/inward/record.url?scp=84859303121&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84859303121
SN - 9783034601733
T3 - Operator Theory: Advances and Applications
SP - 185
EP - 212
BT - Operator Algebras, Operator Theory and Applications - 18th International Workshop on Operator Theory and Applications, 2007
A2 - Labuschagne, L.E.
A2 - Grobler, J.J.
A2 - Möller, M.
PB - Springer International Publishing
T2 - 18th International Workshop on Operator Theory and Applications, IWOTA 2007
Y2 - 3 July 2007 through 6 July 2007
ER -