2-microlocal Besov and Triebel-Lizorkin spaces of variable integrability.
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Henning Kempka (2009)
Revista Matemática Complutense
Malabika Pramanik, Keith M. Rogers, Andreas Seeger (2011)
Studia Mathematica
We prove a Calderón-Zygmund type estimate which can be applied to sharpen known regularity results on spherical means, Fourier integral operators, generalized Radon transforms and singular oscillatory integrals.
G.T. LaVarnway, R. Cooke (2001)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
Guoen Hu, Dachun Yang, Dongyong Yang (2009)
Czechoslovak Mathematical Journal
Let be a nonnegative Radon measure on which only satisfies for all , , with some fixed constants and In this paper, a new characterization for the space of Tolsa in terms of the John-Strömberg sharp maximal function is established.
Yiyu Liang, Dachun Yang, Wen Yuan, Yoshihiro Sawano, Tino Ullrich (2013)
Gala, Sadek, Lahmar-Benbernou, Amina (2007)
Novi Sad Journal of Mathematics
Songqing Chen, Huoxiong Wu, Qingying Xue (2014)
Studia Mathematica
This paper is devoted to investigating the properties of multilinear conditions and conditions, which are suitable for the study of multilinear operators on Lebesgue spaces. Some monotonicity properties of and classes with respect to P⃗ and q are given, although these classes are not in general monotone with respect to the natural partial order. Equivalent characterizations of multilinear classes in terms of the linear classes are established. These results essentially improve and extend...
Jiecheng Chen, Xiangrong Zhu (2004)
Studia Mathematica
We prove that for f ∈ L ln⁺L(ℝⁿ) with compact support, there is a g ∈ L ln⁺L(ℝⁿ) such that (a) g and f are equidistributed, (b) for any measurable set E of finite measure.
Hans Triebel (2004)
Banach Center Publications
J. M. Wilson (2002)
Studia Mathematica
We apply a decomposition lemma of Uchiyama and results of the author to obtain good weighted Littlewood-Paley estimates for linear sums of functions satisfying reasonable decay, smoothness, and cancellation conditions. The heart of our application is a combinatorial trick treating m-fold dilates of dyadic cubes. We use our estimates to obtain new weighted inequalities for Bergman-type spaces defined on upper half-spaces in one and two parameters, extending earlier work of R. L. Wheeden and the author....
Yi Wang, Po-Lam Yung (2014)
Journal of the European Mathematical Society
We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space by functions, generalizing a result of Bourgain–Brezis. We then use this to obtain a Gagliardo–Nirenberg inequality for on the Heisenberg group .
Richard Lechner, Markus Passenbrunner (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic grids, specifically adapted to a given combinatorial situation. This method is used to estimate vector-valued operators rearranging martingale difference sequences such as the Haar system.
David Eric Edmunds, Bohumír Opic (2008)
Czechoslovak Mathematical Journal
We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.
Benoît F. Sehba (2014)
Annales Polonici Mathematici
In the two-parameter setting, we say a function belongs to the mean little BMO if its mean over any interval and with respect to any of the two variables has uniformly bounded mean oscillation. This space has been recently introduced by S. Pott and the present author in relation to the multiplier algebra of the product BMO of Chang-Fefferman. We prove that the Cotlar-Sadosky space of functions of bounded mean oscillation is a strict subspace of the mean little BMO.
Erika Tamási (2006)
Revista Matemática Complutense
This paper deals with approximation numbers of the compact trace operator of an anisotropic Besov space into some Lp-space,trΓ: Bpps,a (Rn) → Lp(Γ), s > 0, 1 < p < ∞,where Γ is an anisotropic d-set, 0 < d < n. We also prove homogeneity estimates, a homogeneous equivalent norm and the localization property in Bpps,a.
Jean Esterle, Alexander Volberg (2002)
Annales scientifiques de l'École Normale Supérieure
Yong-Kum Cho, Joonil Kim (2006)
Studia Mathematica
As a natural extension of Sobolev spaces, we consider Hardy-Sobolev spaces and establish an atomic decomposition theorem, analogous to the atomic decomposition characterization of Hardy spaces. As an application, we deduce several embedding results for Hardy-Sobolev spaces.
P. L. Butzer, R. L. Stens, G. Schmeisser (2014)
Banach Center Publications
Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces are no longer valid in larger spaces. However, when a function f is in some sense close to a Bernstein space, then the corresponding relation holds with a remainder or error term. This paper presents a new, unified approach to these errors in terms of the distance of f from . The difficult situation of derivative-free error estimates is also covered.
Dachun Yang (2009)
Revista Matemática Complutense
Beatrice Vedel (2007)
Revista Matemática Complutense
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