Results 1  10
of
14
Isoperimetry and Symmetrization for Logarithmic Sobolev inequalities
 J. Funct. Anal
"... Abstract. Using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic Sobolev inequalities. In particular, we obtain new Gaussian symmetrization inequalities and connect them with logarithmic Sobolev inequalities. Our methods are very general and can b ..."
Abstract

Cited by 11 (6 self)
 Add to MetaCart
(Show Context)
Abstract. Using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic Sobolev inequalities. In particular, we obtain new Gaussian symmetrization inequalities and connect them with logarithmic Sobolev inequalities. Our methods are very general and can be easily adapted to more general contexts.
POINTWISE SYMMETRIZATION INEQUALITIES FOR SOBOLEV FUNCTIONS AND APPLICATIONS
, 2009
"... We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations. ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
(Show Context)
We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations.
SYMMETRIZATION AND SHARP SOBOLEV INEQUALITIES IN METRIC SPACES
, 2008
"... We derive sharp Sobolev inequalities for Sobolev spaces on metric spaces. In particular, we obtain new sharp Sobolev embeddings and FaberKrahn estimates for Hörmander vector fields. ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
We derive sharp Sobolev inequalities for Sobolev spaces on metric spaces. In particular, we obtain new sharp Sobolev embeddings and FaberKrahn estimates for Hörmander vector fields.
Selfimproving SobolevPoincaré inequalities, truncation and symmetrization
 Potential Anal
"... Abstract. In [12] we developed a new method to obtain symmetrization inequalities of Sobolev type for functions in W 1,1 0 (Ω). In this paper we extend our method to Sobolev functions that do not vanish at the boundary. 1. ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
(Show Context)
Abstract. In [12] we developed a new method to obtain symmetrization inequalities of Sobolev type for functions in W 1,1 0 (Ω). In this paper we extend our method to Sobolev functions that do not vanish at the boundary. 1.
Bernués: Factoring Sobolev inequalities through classes of functions
"... Abstract. We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis,
Boundedness of maximal operators and oscillation of functions . . .
"... In this dissertation the action of maximal operators and the properties of oscillating functions are studied in the context of doubling measure spaces. The work consists of four articles, in which boundedness of maximal operators is studied in several function spaces and different aspects of the o ..."
Abstract
 Add to MetaCart
In this dissertation the action of maximal operators and the properties of oscillating functions are studied in the context of doubling measure spaces. The work consists of four articles, in which boundedness of maximal operators is studied in several function spaces and different aspects of the oscillation of functions are considered. In particular, new characterizations for the BMO and the weak L ∞ are obtained.
Interpolation characterization of the . . .
, 2007
"... Let X be a rearrangementinvariant Banach function space. We calculate the Kfunctionals for the pairs (X, V 1 X) and (X, SX(t − 1 n)), where V 1 X is the reduced Sobolev space built upon X and SX(t − 1 n) is a particular instance of the space SX(w), determined, for a measurable nonnegative functio ..."
Abstract
 Add to MetaCart
Let X be a rearrangementinvariant Banach function space. We calculate the Kfunctionals for the pairs (X, V 1 X) and (X, SX(t − 1 n)), where V 1 X is the reduced Sobolev space built upon X and SX(t − 1 n) is a particular instance of the space SX(w), determined, for a measurable nonnegative function (weight) w by the norm ‖f‖S X (w) = ‖(f ∗ ∗ − f ∗)w‖ X where X is the representation space of X. Using this result, we characterize the rearrangementinvariant hull of a generalized Besov space built upon a pair of r.i. spaces.