On weak Hessian determinants
We consider and study several weak formulations of the Hessian determinant, arising by formal integration by parts. Our main concern are their continuity properties. We also compare them with the Hessian measure.
On weighted estimated for some systems of partial differential operators
Ondelettes, espaces d’interpolation et applications
Nous établissons des résultats d’interpolation non-standards entre les espaces de Besov et les espaces et , avec des applications aux lemmes de régularité en moyenne et aux inégalités de type Gagliardo-Nirenberg. La preuve de ces résultats utilise les décompositions dans des bases d’ondelettes.
Ondelettes et espaces de Besov.
Opérateurs de type Rademacher entre espaces de Banach
Opérateurs pseudo-différentiels et asymptotique sur des variétés à singularités
Opérateurs uniformément convexifiants
Optimal embeddings of critical Sobolev-Lorentz-Zygmund spaces
We establish the embedding of the critical Sobolev-Lorentz-Zygmund space into the generalized Morrey space with an optimal Young function Φ. As an application, we obtain the almost Lipschitz continuity for functions in . O’Neil’s inequality and its reverse play an essential role in the proofs of the main theorems.
Optimal embeddings of generalized homogeneous Sobolev spaces
We prove optimal embeddings of homogeneous Sobolev spaces built over function spaces in ℝⁿ with K-monotone and rearrangement invariant norm into other rearrangement invariant function spaces. The investigation is based on pointwise and integral estimates of the rearrangement or the oscillation of the rearrangement of f in terms of the rearrangement of the derivatives of f.
Optimal Orlicz-Sobolev embeddings.
Optimal reconstruction of derivatives on the Sobolev classes.
Optimal Sobolev embeddings on Rn.
We study Sobolev-type embeddings involving rearrangement-invariant norms. In particular, we focus on the question when such embeddings are optimal. We concentrate on the case when the functions involved are defined on Rn. This subject has been studied before, but only on bounded domains. We first establish the equivalence of the Sobolev embedding to a new type of inequality involving two integral operators. Next, we show this inequality to be equivalent to the boundedness of a certain Hardy operator...
Optimal Sobolev imbedding spaces
This paper continues our study of Sobolev-type imbedding inequalities involving rearrangement-invariant Banach function norms. In it we characterize when the norms considered are optimal. Explicit expressions are given for the optimal partners corresponding to a given domain or range norm.
Optimal stopping and impulsive control of one-dimensional diffusion processes
Optimality of embeddings of Bessel-potential-type spaces into generalized Hölder spaces.
We establish the sharpness of embedding theorems for Bessel-potential spaces modelled upon Lorentz-Karamata spaces and we prove the non-compactness of such embeddings. Target spaces in our embeddings are generalized Hölder spaces. As consequences of our results, we get continuous envelopes of Bessel-potential spaces modelled upon Lorentz-Karamata spaces.
Original title unknown
Orlicz spaces, α-decreasing functions, and the Δ₂ condition
We prove some quantitatively sharp estimates concerning the Δ₂ and ∇₂ conditions for functions which generalize known ones. The sharp forms arise in the connection between Orlicz space theory and the theory of elliptic partial differential equations.
Orlicz-Sobolev spaces with zero boundary values on metric spaces.
Oscillatory kernels in certain Hardy-type spaces
We consider a convolution operator Tf = p.v. Ω ⁎ f with , where K(x) is an (n,β) kernel near the origin and an (α,β), α ≥ n, kernel away from the origin; h(x) is a real-valued function on . We give a criterion for such an operator to be bounded from the space into itself.