Permanence of metric fractals.
Poincaré inequalities and Sobolev spaces.
Our understanding of the interplay between Poincaré inequalities, Sobolev inequalities and the geometry of the underlying space has changed considerably in recent years. These changes have simultaneously provided new insights into the classical theory and allowed much of that theory to be extended to a wide variety of different settings. This paper reviews some of these new results and techniques and concludes with an example on the preservation of Sobolev spaces by the maximal function.[Proceedings...
Poincaré inequalities for powers and products of admissible weights.
Poincaré inequalities for the Heisenberg group target.
Poincaré inequalities with Luxemburg norms in -averaging domains.
Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals
Given a nondegenerate harmonic structure, we prove a Poincaré-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajłasz-Sobolev spaces on nested fractals. In particular, we describe how the "weak"-type gradient on nested fractals relates to the upper gradient defined in the context of general metric spaces.
Pointwise and integral estimates for the -Riesz potential in terms of -maximal and -fractional maximal functions.
Pointwise estimates for a class of strongly degenerate elliptic operators : a geometrical approach
Pointwise inequalities and approximation in fractional Sobolev spaces
We prove that a function belonging to a fractional Sobolev space may be approximated in capacity and norm by smooth functions belonging to , 0 < m + λ < α. Our results generalize and extend those of [12], [4], [14], and [11].
Pointwise inequalities for Sobolev functions and some applications
We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer’s theorem which states that Sobolev functions can be approximated by functions both in norm and capacity.
Pointwise multiplication in Triebel-Lizorkin spaces.
Pointwise multiplicative inequalities and Nirenberg type estimates in weighted Sobolev spaces
Pointwise multipliers of Besov spaces of continuous functions.
Pointwise multipliers on weighted BMO spaces
Let E and F be spaces of real- or complex-valued functions defined on a set X. A real- or complex-valued function g defined on X is called a pointwise multiplier from E to F if the pointwise product fg belongs to F for each f ∈ E. We denote by PWM(E,F) the set of all pointwise multipliers from E to F. Let X be a space of homogeneous type in the sense of Coifman-Weiss. For 1 ≤ p < ∞ and for , we denote by the set of all functions such that , where B(a,r) is the ball centered at a and of...
Polynomial approximation and twenty years later.
Polynomial asymptotics and approximation of Sobolev functions
We prove several results concerning density of , behaviour at infinity and integral representations for elements of the space .
Preduals of Sobolev-Campanato spaces
We present definitions of Banach spaces predual to Campanato spaces and Sobolev-Campanato spaces, respectively, and we announce some results on embeddings and isomorphisms between these spaces. Detailed proofs will appear in our paper in Math. Nachr.
Prescribing the jacobian determinant in Sobolev spaces
Problème de Cauchy global pour des systèmes de Dirac-Klein-Gordon
Problème de Dirichlet dans un cône avec paramètre spectral pour une classe d'espaces de Sobolev à poids