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 -