ALGEBRAS OF SINGULAR INTEGRAL-OPERATORS WITH PIECEWISE CONTINUOUS COEFFICIENTS ON REFLEXIVE ORLICZ SPACES

Authors
Citation
A. Yu, ALGEBRAS OF SINGULAR INTEGRAL-OPERATORS WITH PIECEWISE CONTINUOUS COEFFICIENTS ON REFLEXIVE ORLICZ SPACES, Mathematische Nachrichten, 179, 1996, pp. 187-222
Citations number
41
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
ISSN journal
0025584X
Volume
179
Year of publication
1996
Pages
187 - 222
Database
ISI
SICI code
0025-584X(1996)179:<187:AOSIWP>2.0.ZU;2-R
Abstract
We consider singular integral operators with piecewise continuous coef ficients on reflexive Orlicz spaces L(M)(Gamma), which are generalizat ions of the Lebesgue spaces L(p)(Gamma), 1 < p < infinity. We suppose that Gamma belongs to a large class of Carleson curves, including curv es with corners and cusps as well as curves that look locally like two logarithmic spirals scrolling up at the same point. For the singular integral operator associated with the Riemann boundary value problem w ith a piecewise continuous coefficient G, we establish a Fredholm crit erion and an index formula in terms of the essential range of G comple mented by spiralic horns depending on the Boyd indices of L(M)(Gamma) and contour properties. Our main result is a symbol calculus for the c losed algebra of singular integral operators with piecewise continuous matrix-valued coefficients on L(M)(n)(Gamma).