Compact Difference of Fejér-Riesz Composition Operators

초록

We introduce the Fej & eacute;r-Riesz composition operator F-phi induced by a holomorphic self-map phi of the unit disk D, and defined on the space of holomorphic functions on D by F(phi)f= chi((-1,1))f degrees phi. Denote by A(alpha )(p)the standard weighted Bergman space of holomorphic functions on D and denote the Hardy space H-p by A(-1)(p). We study the operators F-phi:A(alpha)(p)-> L-p(m(alpha)),where m(alpha) is the weighted Lebesgue measure dm(alpha)(x)=(1-x(2))(alpha+1)dx, x is an element of(-1,1).For 0< p =-1, every suchF(phi) is bounded, which in the case alpha=-1 is related to the classical Fej & eacute;r-Riesz Inequality. We provide characterizations for when F-phi is compact and for when F-phi-F-psi is compact

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