TY - JOUR

T1 - Distorted Hankel integral operators

AU - Peller, V. V.

AU - Александров, Алексей Борисович

PY - 2004

Y1 - 2004

N2 - For α, β > 0 and for a locally integrable function (or, more generally, a distribution) ψ on (0, ∞), we study the integral operators script G signψα,β on L 2 (ℝ+) defined by (script G signψ α,β f)(x) = ∫ℝ+ ψ(x α + yβ)f(y) dy. We describe the bounded and compact operators script G signψα,β and the operators script G signψα,β of Schatten-von Neumann class Sp. The main results of the paper are given in Section 5, where we study continuity properties of the averaging projection script Q signα,β onto the operators of the form script G signψα,β. In particular, we show that if α ≤ β and β > 1, then script G sign ψα,β is bounded on Sp if and only if 2β(β + 1)-1 < p < 2β(β - 1) -1.

AB - For α, β > 0 and for a locally integrable function (or, more generally, a distribution) ψ on (0, ∞), we study the integral operators script G signψα,β on L 2 (ℝ+) defined by (script G signψ α,β f)(x) = ∫ℝ+ ψ(x α + yβ)f(y) dy. We describe the bounded and compact operators script G signψα,β and the operators script G signψα,β of Schatten-von Neumann class Sp. The main results of the paper are given in Section 5, where we study continuity properties of the averaging projection script Q signα,β onto the operators of the form script G signψα,β. In particular, we show that if α ≤ β and β > 1, then script G sign ψα,β is bounded on Sp if and only if 2β(β + 1)-1 < p < 2β(β - 1) -1.

KW - Averaging projection

KW - Besov spaces

KW - Hankel operator

KW - Schatten classes

UR - http://www.scopus.com/inward/record.url?scp=8844226700&partnerID=8YFLogxK

U2 - 10.1512/iumj.2004.53.2525

DO - 10.1512/iumj.2004.53.2525

M3 - Article

VL - 53

SP - 925

EP - 940

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 4

ER -