On the weighted inequality between the Gagliardo and Sobolev seminorms

Ritva Hurri Syrjänen; Javier C. Martínez-Perales; Carlos Pérez; Antti V. Vähäkangas

doi:10.1007/s11856-025-2834-y

November 18, 2025Israel Journal of MathematicsOpen Access

On the weighted inequality between the Gagliardo and Sobolev seminorms

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Key Points

Weighted inequalities were improved in the context of Gagliardo and Sobolev seminorms, enhancing previous techniques.
Key contributions involved results building on work by Bourgain, Brezis, and Mironescu to refine mathematical bounds.
The analysis focused on A 1 weights to establish clearer relationships between seminorms and their applications.
Potential implications include better understanding of functional inequalities in mathematical analysis and related fields.

Implication

Analysis reveals enhanced inequalities in Gagliardo and Sobolev seminorms with A 1 weights, suggesting improved mathematical frameworks.

Abstract

We prove weighted inequalities between the Gagliardo and Sobolev seminorms. With A 1 weights we improve earlier results of Bourgain, Brezis, and Mironescu.

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Cite This Study

Syrjänen et al. (2025) studied this question.

synapsesocial.com/papers/692509ddc0ce034ddc3521ef https://doi.org/10.1007/s11856-025-2834-y

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On the weighted inequality between the Gagliardo and Sobolev seminorms

Key Points

Implication

Abstract

Discussion

Cite This Study

On the weighted inequality between the Gagliardo and Sobolev seminorms

Key Points

Implication

Abstract

Discussion

Cite This Study

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