Let K be a distribution on R^2. We denote by λ(K) the twisted convolution operator f → K × f defined by the formula K × f(x, y) = ∫∫ du dv K(x − u, y − v) f(u, v) exp(ixv − iyu). We show that there exists K such that the operator λ(K) is bounded on L^p(R^2) for every p in (1, 2], but is unbounded on L^q(R^2) for every q > 2.
Asymmetry of twisted convolution operators
MANTERO, ANNA MARIA
1982-01-01
Abstract
Let K be a distribution on R^2. We denote by λ(K) the twisted convolution operator f → K × f defined by the formula K × f(x, y) = ∫∫ du dv K(x − u, y − v) f(u, v) exp(ixv − iyu). We show that there exists K such that the operator λ(K) is bounded on L^p(R^2) for every p in (1, 2], but is unbounded on L^q(R^2) for every q > 2.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
