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math.FA2026
Generalized Sobolev-Orlicz spaces based on the Riesz fractional gradient as interpolation and potential spaces
Pedro Miguel Campos, Guillermo García-Sáez
In this work we establish that the recently introduced fractional Sobolev spaces based on the Riesz fractional gradient of Musielak-Orlicz functions by one of the authors, coincide…
math.FA2025
Compact embeddings of Bessel Potential Spaces
José C. Bellido, Javier Cueto, Guillermo García-Sáez
Bessel potential spaces have gained renewed interest due to their robust structural properties and applications in fractional partial differential equations (PDEs). These spaces, d…
math.FA2025
Bessel Potential Spaces and Complex Interpolation: Continuous embeddings
José Carlos Bellido, Guillermo García-Sáez
Bessel potential spaces, introduced in the 1960s, are derived through complex interpolation between Lebesgue and Sobolev spaces, making them intermediate spaces of fractional diffe…