Image of under the Hermite semigroup.
We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, and , , under the Dunkl-Hermite semigroup. Also, we consider the image of the space of tempered distributions and we give Paley-Wiener type theorems for the transforms given by the Dunkl-Hermite semigroup.
By a variant of the standard good λ inequality, we prove the Muckenhoupt-Wheeden inequality for measures which are not necessarily in the Muckenhoupt class. Moreover we can deal with a general potential operator, and consequently we obtain a suitable approach to the two weight inequality for such an operator when one of the weight functions satisfies a reverse doubling condition.
The paper deals with covering problems and the degree of compactness of operators. The main part is devoted to relationships between entropy moduli and Kolmogorov (resp. Gelfand and approximation) numbers for operators which may be interpreted as counterparts to the classical Bernstein-Jackson inequalities for functions. Certain quantifications of results in the Riesz-Schauder-Theory are given. Finally, the largest distance between “the degree of approximation” and the “degree of compactness” of...
In this paper, we prove that every unbounded linear operator satisfying the Korotkov-Weidmann characterization is unitarily equivalent to an integral operator in L 2(R), with a bounded and infinitely smooth Carleman kernel. The established unitary equivalence is implemented by explicitly definable unitary operators.