5 citations · 16 across the 9 of their papers we have counts for
6 papers · 1 filter
A unified approach to inequalities for K-functionals and moduli of smoothness
Amiran Gogatishvili, Bohumir Opic, Sergey Tikhonov +1
The paper provides a detailed study of crucial inequalities for smoothness and interpolation characteristics in rearrangement invariant Banach function spaces. We present a unified…
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…
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…