6 citations · 9 across the 6 of their papers we have counts for
10 papers
Quantitative -Convergence: A Variational Extrapolation Framework
Oscar Dominguez, Mario Milman
This paper introduces a new extrapolation framework within the Calculus of Variations. We develop a robust quantitative theory of the -convergence approach of De Giorgi by combi…
Blow-up at finite time for the generalized SQG equations in the Sobolev well-posedness regime
Diego Córdoba, Óscar Domínguez, José Lucas-Manchón +1
We prove finite-time singularity formation for the forced generalized surface quasi-geostrophic equation in the singular velocity regime , where corresponds to SQG…
A sparse resolution of the DiPerna-Majda gap problem for D Euler equations
Oscar Domínguez, Daniel Spector
A central question which originates in the celebrated work in the 1980's of DiPerna and Majda asks what is the optimal decay such that uniform rates of…
A sharp stability criterion for Euler equations via sparseness
Óscar Domínguez, Mario Milman
We introduce sparse versions of function spaces that are relevant to characterize the solutions of Euler equations without concentration. The standard Sobolev space is giv…
Truncated smooth function spaces
Oscar Domínguez, Sergey Tikhonov
We introduce truncated Besov and Triebel--Lizorkin function spaces and investigate their main properties: embeddings, interpolation, duality, lifting, traces. These new scales allo…
Bourgain-Brezis-Mironescu-Maz'ya-Shaposhnikova limit formulae for fractional Sobolev spaces via interpolation and extrapolation
Oscar Domínguez, Mario Milman
The real interpolation spaces between and (resp. ), are characterized in terms of fra…
New estimates for the maximal functions and applications
Oscar Domínguez, Sergey Tikhonov
In this paper we study sharp pointwise inequalities for maximal operators. In particular, we strengthen DeVore's inequality for the moduli of smoothness and a logarithmic variant o…
Embeddings and characterizations of Lipschitz spaces
Oscar Domínguez, Dorothee D. Haroske, Sergey Tikhonov
In this paper we give a thorough study of Lipschitz spaces. We obtain the following new results: (1) Sharp Jawerth-Franke-type embeddings between the Besov and Lipschitz spaces ext…
Sobolev embeddings, extrapolations, and related inequalities
Oscar Domínguez, Sergey Tikhonov
In this paper we propose a unified approach, based on limiting interpolation, to investigate the embeddings for the Sobolev space $(\dot{W}^k_p(\mathcal{X}))_0, \, \mathcal{X} \in…
Function spaces of logarithmic smoothness: embeddings and characterizations
Oscar Domínguez, Sergey Tikhonov
In this paper we present a comprehensive treatment of function spaces with logarithmic smoothness (Besov, Sobolev, Triebel-Lizorkin). We establish the following results: Sharp embe…