Generalized Riesz projections and Toeplitz operators

Abstract

Let 1 < p < ∞ .In this paper, for a measurable function v and a weight function w , the generalized Riesz projection P v is defined by. If P 0 is the self-adjoint projection from L 2 (w) onto H 2 (w) , then P 0 = P α for some outer function α satisfying w = |α| -2 .In this paper, P v on L p (w) is studied.As an application, the invertibility criterion for the generalized Toeplitz operator T v φ and the generalized singular integral operator φP v + Q v , Q v = I -P v are investigated using the weighted norm inequality.The operator norm inequality for the generalized Hankel operator H v φ is also presented.

Locations

• Mathematical Inequalities & Applications - View - PDF