SOME REMARKS ON BOUNDARY OPERATORS OF BESSEL EXTENSIONS

Abstract

In this paper we study some boundary operators of a class of Bessel-type Littlewood-Paley extensions whose prototype is Delta(x)u(x,y) +(1-2s)(y) (partial derivative u)(partial derivative y)(x,y) + (2)(partial derivative y) (partial derivative 2u)(x,y) = 0 for x is an element of R-d,y > 0, u(x,0) = f(x) for x is an element of R-d. In particular, we show that with a logarithmic scaling one can capture the failure of analyticity of these extensions in the limiting cases s = k is an element of N.