Results 41 to 50 of about 2,173 (142)

Integro-differential systems with variable exponents of nonlinearity

Open Mathematics, 2017
Some nonlinear integro-differential equations of fourth order with variable exponents of the nonlinearity are considered. The initial-boundary value problem for these equations is investigated and the existence theorem for the problem is proved.
Buhrii Oleh, Buhrii Nataliya
doaj   +1 more source

A note on the fractional perimeter and interpolation [PDF]

, 2017
We present the fractional perimeter as a set-function interpolation between the Lebesgue measure and the perimeter in the sense of De Giorgi. Our motivation comes from a new fractional Boxing inequality that relates the fractional perimeter and the ...
Ponce, Augusto C., Spector, Daniel
core   +3 more sources

Approximation numbers of Sobolev embeddings of radial functions on isotropic manifolds

Journal of Function Spaces, Volume 5, Issue 1, Page 27-48, 2007., 2007
We regard the compact Sobolev embeddings between Besov and Sobolev spaces of radial functions on noncompact symmetric spaces of rank one. The asymptotic formula for the behaviour of approximation numbers of these embeddings is described.
Leszek Skrzypczak, Bernadeta Tomasz, Hans Triebel   +2 more
wiley   +1 more source

A direct proof of Sobolev embeddings for quasi‐homogeneous Lizorkin–Triebel spaces with mixed norms

Journal of Function Spaces, Volume 5, Issue 2, Page 183-198, 2007., 2007
The article deals with a simplified proof of the Sobolev embedding theorem for Lizorkin–Triebel spaces (that contain the Lp‐Sobolev spaces Hps as special cases). The method extends to a proof of the corresponding fact for general Lizorkin–Triebel spaces based on mixed Lp‐norms.
Jon Johnsen, Winfried Sickel, Jürgen Appell   +2 more
wiley   +1 more source

Regularity for commutators of the local multilinear fractional maximal operators

Advances in Nonlinear Analysis, 2020
In this paper we introduce and study the commutators of the local multilinear fractional maximal operators and a vector-valued function b⃗ = (b1, …, bm). Under the condition that each bi belongs to the first order Sobolev spaces, the bounds for the above
Zhang Xiao, Liu Feng
doaj   +1 more source

Hölder Inequalities and Sharp Embeddings in Function Spaces of $B^s_{pq}$ and $F^s_{pq}$ Type

, 1995
where in that special case c = 1 may be chosen. With exception of Subsection 1.2, all spaces in this paper are defined on R . This justifies to omit R in the sequel.
W. Sickel, H. Triebel
semanticscholar   +1 more source

On the variation of the discrete maximal operator

, 2020
In this note we study the endpoint regularity properties of the discrete nontangential fractional maximal operator Mα,β f (n) = sup r∈N |m−n| β r 1 (2r +1)1−α r ∑ k=−r | f (m+ k)|, where α ∈ [0,1) , β ∈ [0,∞) and N = {0,1,2, . . .
Feng Liu
semanticscholar   +1 more source

New classes of rearrangement‐invariant spaces appearing in extreme cases of weak interpolation

Journal of Function Spaces, Volume 4, Issue 3, Page 275-304, 2006., 2006
We study weak type interpolation for ultrasymmetric spaces L?,E i.e., having the norm ??(t)f*(t)?E˜, where ?(t) is any quasiconcave function and E˜ is arbitrary rearrangement‐invariant space with respect to the measure d t /t. When spaces L?,E are not “too close” to the endpoint spaces of interpolation (in the sense of Boyd), the optimal interpolation ...
Evgeniy Pustylnik, Teresa Signes, Fernando Cobos   +2 more
wiley   +1 more source

Modulation spaces Mp,q for 0 < p, q?8

Journal of Function Spaces, Volume 4, Issue 3, Page 329-341, 2006., 2006
The purpose of this paper is to construct modulation spaces Mp,q(Rd) for general 0 < p, q?8, which coincide with the usual modulation spaces when 1?p,q?8, and study their basic properties including their completeness. Given any g?S(Rd) such that supp g ???{?||?|?1} and ?k?Zd g (?-ak)=1, our modulation space consists of all tempered distributions f such
Masaharu Kobayashi, Hans Triebel
wiley   +1 more source

Sobolev subspaces of nowhere bounded functions [PDF]

, 2016
We prove that in any Sobolev space which is subcritical with respect to the Sobolev Embedding Theorem there exists a closed infinite dimensional linear subspace whose non zero elements are nowhere bounded functions.
Lamberti, PIER DOMENICO, Stefani, Giorgio   +1 more
core   +3 more sources