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Extremals in Hardy-Littlewood-Sobolev inequalities for stable processes

Publicated to:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 507 (1): 125742- - 2022-03-01 507(1), DOI: 10.1016/j.jmaa.2021.125742

Authors: de Pablo, Arturo; Quiros, Fernando; Ritorto, Antonella

Affiliations

Katholische Univ Eichstatt Ingolstadt, Math Geograph Fak, D-85071 Eichstatt, Germany - Author
Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain - Author
Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain - Author

Abstract

We prove the existence of an extremal function in the Hardy-Littlewood-Sobolev inequality for the energy associated to an stable operator. To this aim we obtain a concentration-compactness principle for stable processes in RN.

Keywords

alpha-stable processescalculusconcaveelliptic problems with criticalelliptic-equationsnonlinearitiesAlpha-stable processesConcentration-compactness principleElliptic problems with criticalElliptic problems with critical nonlinearitiesNonlinearitiesΑ–stable processes

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2022, it was in position , thus managing to position itself as a Q1 (Primer Cuartil), in the category Analysis.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.56. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Field Citation Ratio (FCR) from Dimensions: 1.67 (source consulted: Dimensions Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-27, the following number of citations:

  • WoS: 2
  • Scopus: 2

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-27:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 1 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Germany.