Results 41 to 50 of about 2,147 (138)

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

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

The Lusin Theorem and Horizontal Graphs in the Heisenberg Group

Analysis and Geometry in Metric Spaces, 2013
In this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz ...
Hajłasz Piotr, Mirra Jacob
doaj   +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

Admissibility versus Ap-Conditions on Regular Trees

Analysis and Geometry in Metric Spaces, 2020
We show that the combination of doubling and (1, p)-Poincaré inequality is equivalent to a version of the Ap-condition on rooted K-ary trees.
Nguyen Khanh Ngoc, Wang Zhuang
doaj   +1 more source

On one extension theorem dealing with weighted Orlicz-Slobodetskii space. Analysis on Lipschitz subgraph and Lipschitz domain

, 2016
Having a given weight ρ(x) = τ (dist(x,∂Ω)) defined on Lipschitz boundary domain Ω and an Orlicz function Ψ , we construct the subordinated weight ω(·, ·) defined on ∂Ω×∂Ω and extension operator ExtL : Lip(∂Ω) → Lip(Ω) form Lipschitz functions defined on
A. Kałamajska, R. Dhara
semanticscholar   +1 more source

Characterization of Riesz and Bessel potentials on variable Lebesgue spaces

Journal of Function Spaces, Volume 4, Issue 2, Page 113-144, 2006., 2006
Riesz and Bessel potential spaces are studied within the framework of the Lebesgue spaces with variable exponent. It is shown that the spaces of these potentials can be characterized in terms of convergence of hypersingular integrals, if one assumes that the exponent satisfies natural regularity conditions. As a consequence of this characterization, we
Alexandre Almeida, Stefan Samko, Vakhtang Kokilashvili   +2 more
wiley   +1 more source

Hardy–Adams Inequalities on ℍ2 × ℝn-2

Advanced Nonlinear Studies, 2021
Let ℍ2{\mathbb{H}^{2}} be the hyperbolic space of dimension 2. Denote by Mn=ℍ2×ℝn-2{M^{n}=\mathbb{H}^{2}\times\mathbb{R}^{n-2}} the product manifold of ℍ2{\mathbb{H}^{2}} and ℝn-2(n≥3){\mathbb{R}^{n-2}(n\geq 3)}.
Ma Xing, Wang Xumin, Yang Qiaohua
doaj   +1 more source

Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz‐Sobolev embeddings

Journal of Function Spaces, Volume 3, Issue 2, Page 183-208, 2005., 2005
Let Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x ∈ Ω ⊂ ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A = Lφ,E, B = Lψ,E, giving some optimal (or rather sharp) relations between ...
Evgeniy Pustylnik, Lech Maligranda
wiley   +1 more source