Results 1  10
of
1,613
NOTE ON THE SUPPORT OF SOBOLEV FUNCTIONS
"... We prove a topological restriction on the support of Sobolev functions. Let k and n be integers such that 0 Ú k Ú n, and suppose that p Ù 1 and THEOREM. p Ù k 1. Then the only distribution in the Sobolev space W1,p(Rn) which is supported by a kcell is the zero distribution. Here the Sobolev space W ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We prove a topological restriction on the support of Sobolev functions. Let k and n be integers such that 0 Ú k Ú n, and suppose that p Ù 1 and THEOREM. p Ù k 1. Then the only distribution in the Sobolev space W1,p(Rn) which is supported by a kcell is the zero distribution. Here the Sobolev space
On the representation of mutilated Sobolev functions
, 1999
"... We show that ridgelets, a system introduced in [4], are optimal to represent smooth multivariate functions that may exhibit linear singularities. For instance, let {u · x − b> 0} be an arbitrary hyperplane and consider the singular function f(x) = 1 {u·x−b>0}g(x), where g is compactly support ..."
Abstract

Cited by 13 (5 self)
 Add to MetaCart
We show that ridgelets, a system introduced in [4], are optimal to represent smooth multivariate functions that may exhibit linear singularities. For instance, let {u · x − b> 0} be an arbitrary hyperplane and consider the singular function f(x) = 1 {u·x−b>0}g(x), where g is compactly
A boundary uniqueness property for weighted Sobolev functions
 HIROSHIMA MATH. J. 31 (2001), 439–449
, 2001
"... The aim of this paper is to discuss a uniqueness property for Sobolev functions with certain condition on area integrals. ..."
Abstract
 Add to MetaCart
The aim of this paper is to discuss a uniqueness property for Sobolev functions with certain condition on area integrals.
POINTWISE CHARACTERIZATIONS OF HARDYSOBOLEV FUNCTIONS
, 2006
"... Abstract. We establish pointwise characterizations of functions in the HardySobolev spaces H 1,p within the range p ∈ (n/(n + 1), 1]. In particular, a locally integrable function u belongs to H 1,p (R n) if and only if u ∈ L p (R n) and it satisfies the Hajlasz type condition u(x) − u(y)  ≤ x ..."
Abstract

Cited by 22 (4 self)
 Add to MetaCart
Abstract. We establish pointwise characterizations of functions in the HardySobolev spaces H 1,p within the range p ∈ (n/(n + 1), 1]. In particular, a locally integrable function u belongs to H 1,p (R n) if and only if u ∈ L p (R n) and it satisfies the Hajlasz type condition u(x) − u(y)  ≤ x
Integral representations of functions and continuity properties of Sobolev functions
, 2003
"... We ¯rst introduce Sobolev's integral representation for smooth functions with compact support. To extend it to Sobolev functions in the class Wm;p(Rn), we modify the kernel functions appearing in the representation by use of Taylor's remainders. As an application of modi¯ed integral repr ..."
Abstract
 Add to MetaCart
We ¯rst introduce Sobolev's integral representation for smooth functions with compact support. To extend it to Sobolev functions in the class Wm;p(Rn), we modify the kernel functions appearing in the representation by use of Taylor's remainders. As an application of modi¯ed integral
Measure density and extendability of Sobolev functions
"... We study necessary and sufficient conditions for a domain to be a Sobolev extension domain in the setting of metric measure spaces. In particular, we prove that extension domains must satisfy a measure density condition. 1. ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
We study necessary and sufficient conditions for a domain to be a Sobolev extension domain in the setting of metric measure spaces. In particular, we prove that extension domains must satisfy a measure density condition. 1.
On the CalderónZygmund lemma for Sobolev functions
, 2008
"... We correct an inaccuracy in the proof of a result in [Aus1]. 2000 MSC: 42B20, 46E35 Key words: CalderónZygmund decomposition; Sobolev spaces. We recall the lemma. Lemma 0.1. Let n ≥ 1, 1 ≤ p ≤ ∞ and f ∈ D ′ (R n) be such that ‖∇f‖p < ∞. Let α> 0. Then, one can find a collection of cubes (Qi) ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We correct an inaccuracy in the proof of a result in [Aus1]. 2000 MSC: 42B20, 46E35 Key words: CalderónZygmund decomposition; Sobolev spaces. We recall the lemma. Lemma 0.1. Let n ≥ 1, 1 ≤ p ≤ ∞ and f ∈ D ′ (R n) be such that ‖∇f‖p < ∞. Let α> 0. Then, one can find a collection of cubes (Qi
SHARP EXPONENTIAL INTEGRABILITY FOR TRACES OF MONOTONE SOBOLEV FUNCTIONS
, 2007
"... Abstract. We answer a question posed in [12] on exponential integrability of functions of restricted nenergy. We use geometric methods to obtain a sharp exponential integrability result for boundary traces of monotone Sobolev functions defined on the unit ball. 1. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We answer a question posed in [12] on exponential integrability of functions of restricted nenergy. We use geometric methods to obtain a sharp exponential integrability result for boundary traces of monotone Sobolev functions defined on the unit ball. 1.
Results 1  10
of
1,613