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.
Original language | English |
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Pages (from-to) | 925-940 |
Number of pages | 16 |
Journal | Indiana University Mathematics Journal |
Volume | 53 |
Issue number | 4 |
DOIs | |
State | Published - 2004 |
Externally published | Yes |
ID: 5204514