Hans Triebel

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math.FA2024

Mapping properties of the Fourier transform in spaces with dominating mixed smoothness

Hans Triebel

This paper deals with continuous and compact mappings of the Fourier transform in function spaces with dominating mixed smoothness.

math.FA2023

Mapping properties of Fourier transforms, revisited

Dorothee D. Haroske, Leszek Skrzypczak, Hans Triebel

The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished Besov spaces $B_{p}^{s} (R^{n}) = B_{p, p}^{s} (R^{n})$ , $1\le p…

math.FA2023

A note on Hausdorff-Young inequalities in function spaces

Hans Triebel

The classical Hausdorff-Young inequalities for the Fourier transform acting between appropriate $L_{p}$ spaces are cornerstones of Fourier analysis. Here we extend it to weighted spa…

math.FA2022

Quarkonial analysis

Hans Triebel

The spaces $A_{p, q}^{s} (R^{n})$ with $A \in {B, F}$ , $s \in R$ and $0 < p, q \leq \infty$ are usually introduced in terms of Fourier--analytical decompositions. Relate…

math.FA2022

Truncations and compositions in function spaces

Hans Triebel

These notes deal with some recent assertions about truncations $f \mapsto ∣ f ∣$ and compositions $f \mapsto g \circ f$ in the spaces $A_{p, q}^{s} (R^{n})$ , $A \in {B, F}$ .

math.FA2021

Mapping properties of Fourier transforms

Hans Triebel

The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished function spaces on $R^{n}$ . The degree of compactness will be m…