Sobolev spaces in the generalized distribution spaces of Beurling type

Generalized Dunkl-sobolev Spaces of Exponential Type and Applications

We study the Sobolev spaces of exponential type associated with the Dunkl-Bessel Laplace operator. Some properties including completeness and the imbedding theorem are proved. We next introduce a class of symbols of exponential type and the associated pseudodifferential-difference operators, which naturally act on the generalized Dunkl-Sobolev spaces of exponential type. Finally, using the theo...

Sobolev Spaces

A Beurling-helson Type Theorem for Modulation Spaces

We prove a Beurling-Helson type theorem on modulation spaces. More precisely, we show that the only C changes of variables that leave invariant the modulation spaces M(R) are affine functions on R. A special case of our result involving the Sjöstrand algebra was considered earlier by A. Boulkhemair.

Generalized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces

Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|begin{align*}left|f right|_{mathcal{W}_...

Generalized composition operators from logarithmic Bloch type spaces to Q_K type spaces

In this paper boundedness and compactness of generalized composition oper-ators from logarithmic Bloch type spaces to Q_K type spaces are investigated.