Distorted Hankel integral operators
Aleksandrov, A. B. · Peller, V. V.
Functional Analysis
Classical Analysis and ODEs
Combinatorics
Category Theory
Complex Variables
47B35, 47G10, 46E, 46F
الأصل · EN
For,>0 and for a locally integrable function (or, more generally, a distribution) on (0,), we study integral ooperators G, on L²(+) defined by (G, f)(x)=∫₊(x+y)f(y)dy. We describe the bounded and compact operators G, and operators G, of Schatten--von Neumann class ₚ. We also study continuity properties of the averaging projection, onto the operators of the form G,. In particular, we show that if ≤ and >1, then G, is bounded on ₚ if and only if 2(+1)⁻¹<p<2(-1)⁻¹.
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