A convolution operator, bounded on L^q(R^n) is bounded on L^p(R^n), if p and q are conjugate exponents. It is well known that this fact is false if we replace R^n with a general non-commutative locally compact group G. In this paper we give a simple construction of a convolution operator on a suitable compact group G, which is bounded on L^q for every q ≥ 2 and is unbounded on L^p, if p<2
A remark on the asymmetry of convolution operators
GIULINI, SAVERIO
1990-01-01
Abstract
A convolution operator, bounded on L^q(R^n) is bounded on L^p(R^n), if p and q are conjugate exponents. It is well known that this fact is false if we replace R^n with a general non-commutative locally compact group G. In this paper we give a simple construction of a convolution operator on a suitable compact group G, which is bounded on L^q for every q ≥ 2 and is unbounded on L^p, if p<2
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