P. Gurka

collaborators

3 papers

math.FA2025

Quantitative Non-Compactness Properties of the Fourier Transform on Optimal Spaces

David E. Edmunds, Petr Gurka, Jan Lang

We establish that the Fourier transform $F : L^{p} (R^{d}) \to L^{p^{'}, p} (R^{d})$ , for $d \in N$ and $1 < p < 2$ , is not strictly singular, thereby confirming t…

math.FA2025

Quantitative analysis of optimal Sobolev-Lorentz embeddings with $I^\pm$ -homogeneous weights

Petr Gurka, Jan Lang, ZdenÄk Mihula

Optimal weighted Sobolev-Lorentz embeddings with homogeneous weights in open convex cones are established, with the exact value of the optimal constant. These embeddings are non-co…

math.AP2024

Existence of an extremal function of Sobolev critical embedding with an $I^\pm$ -homogeneous weight

Petr Gurka, Daniel Hauer

In our previous publication [{\em Calc. Var. Partial Differential Equations}, 60(1):Paper No. 16, 27, 2021], we delved into examining a critical Sobolev-type embedding of a Sobolev…

Quantitative Non-Compactness Properties of the Fourier Transform on Optimal Spaces

Quantitative analysis of optimal Sobolev-Lorentz embeddings with I^±-homogeneous weights

Existence of an extremal function of Sobolev critical embedding with an I^±-homogeneous weight

Quantitative analysis of optimal Sobolev-Lorentz embeddings with $I^\pm$ -homogeneous weights

Existence of an extremal function of Sobolev critical embedding with an $I^\pm$ -homogeneous weight