Distorted Hankel Integral Operators
نویسنده
چکیده
For α, β > 0 and for a locally integrable function (or, more generally , a distribution) ϕ on (0, ∞), we study integral ooperators G α,β ϕ on L 2 (R +) defined by G α,β ϕ f (x) = R+ ϕ x α + y β f (y)dy. We describe the bounded and compact operators G α,β ϕ and operators G α,β ϕ of Schatten–von Neumann class S p. We also study continuity properties of the averaging projection Q α,β onto the operators of the form G α,β ϕ. In particular, we show that if α ≤ β and β > 1, then G α,β ϕ is bounded on S p if and only if 2β(β + 1) −1 < p < 2β(β − 1) −1 .
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