Anisotropic weak Hardy spaces and interpolation theorems

In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also given. As some applications of the above results, the authors prove some interpolation theorems and obtain the boundedness of the singular integral operators on these Hardy spaces.     

Fixed point theorems and the Ulam–Hyers stability in non-Archimedean cone metric spaces

Let (X,p)$(X,p)$ be a metric space with a K-valued non-Archimedean metric p  . In this paper, we prove the existence and approximation of a fixed point for operators F:X→X$F:X\to X$ satisfying the contractive condition in the form p(F(x),F(y))?Q[p(x,y)]$p(F(x),F(y))?Q[p(x,y)]$, where Q:K→K$Q:K\to K$ is an increasing operator. Then, we study the generalized Ulam–Hyers stability of fixed point equations. We next obtain an extension of the Krasnoselskii fixed point theorem for the sum of two operators. Finally, an application to functional equations is given.     

Denjoy-Wolff theorems for Hilbert’s and Thompson’s metric spaces

We study the dynamics of fixed point free mappings on the interior of a normal, closed cone in a Banach space that are nonexpansive with respect to Hilbert’s metric or Thompson’s metric. We establish several Denjoy-Wolff type theorems which confirm conjectures by Karlsson and Nussbaum for an important class of nonexpansive mappings. We also extend and put into a broader perspective results by Gaubert and Vigeral concerning the linear escape rate of such nonexpansive mappings.     

Spherical spectral synthesis and two-radius theorems on Damek–Ricci spaces

We prove that spherical spectral analysis and synthesis hold in Damek–Ricci spaces and derive two-radius theorems.     

A Weil–Petersson type metric on spaces of metric graphs

In this note, we discuss an analogue of the Weil–Petersson metric for spaces of metric graphs and some of its properties.     

Hardy and Cowling–Price theorems associated with the Jacobi–Cherednik operator

This paper is devoted to the proof of Hardy and Cowling–Price type theorems for the Fourier transform tied to the Jacobi–Cherednik operator.     

Meir–Keeler-type conditions in abstract metric spaces

Various Meir–Keeler-type conditions for mappings acting in abstract metric spaces are presented and their connections are discussed. Results about associated symmetric spaces, obtained in [S. Radenovi?, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (2011), 38–50] are used to show that the regularity condition for the underlying cone can be dropped in some fixed point results that have appeared recently.     

Wandering subspaces and quasi-wandering subspaces in the Hardy–Sobolev spaces

In this paper, we prove that for-1/2 ≤β≤0.suppose M is an invariant subspaces of the Hardy Sobolev spaces H_β~2(D) for T_z~β, then M() zM is a generating wandering subspace of M, that is,M=[MzM]_T_z~β Moreover, any non-trivial invariant subspace M of H_β~2(D) is also generated by the quasi-wandering subspace P_MT_z~βM~⊥ that is,M=[P_MT_z~βM~⊥]_(T_z~β).     

Strong Hardy–Littlewood theorems for analytic functions and mappings of finite distortion

A formula is pointed out that explains why an analytic function often enjoys the same smoothness properties as its modulus. This is extended to quasiregular mappings and, mutatis mutandis, to mappings of finite distortion.Mathematics Subject Classification (1991): 30C65, 30D50, 30D55Supported in part by Grant 02-01-00267 from the Russian Foundation for Fundamental Research, DGICYT Grant BFM2002-04072-C02-01, CIRIT Grant 2001-SGR-00172, by the Ramón y Cajal program (Spain) and by the European Communitys Human Potential Program under contract HPRN-CT-2000-00116 (Analysis and Operators).     

Generalization of the theorems of Barndorff-Nielsen and Balakrishnan–Stepanov to Riesz spaces

Positivity - In a Dedekind complete Riesz space, E, we show that if $$(P_n)$$ is a sequence of band projections in E then $$begin{aligned} limsup limits _{nrightarrow infty } P_n - liminf...     

Fredholmness of multipliers on Hardy–Sobolev spaces

This paper discusses the Fredholmness of multipliers on Hardy–Sobolev Spaces and obtains an index formula for the multipliers with some special symbols. Our results show that Hardy–Sobolev spaces have richer properties than classical holomorphic function spaces, and the behavior of the operators on these spaces is complex. Some methods of Hardy or Bergman spaces fail in the case of the Hardy–Sobolev space.     

Embedding theorems of Besov and Triebel-Lizorkin spaces on spaces of homogeneous type

In this paper, the author establishes the embedding theorems for different metrics of inhomoge-neous Besov and Triebel-Lizorkin spaces on spaces of homogeneous type. As an application, the author obtains some estimates for the entropy numbers of the embeddings in the limiting cases between some Besov spaces and some logarithmic Lebesgue spaces.     

Kotani–Last problem and Hardy spaces on surfaces of Widom type

This is a small theory of non almost periodic ergodic families of Jacobi matrices with purely (however) absolutely continuous spectrum. The reason why this effect may happen is that under our “axioms” we found an analytic condition on the resolvent set that is responsible for (exactly equivalent to) this effect.     

New characterizations of Hajlasz-Sobolev spaces on metric spaces

This paper introduces the fractional Sobolev spaces on spaces of homogeneous type,includingmetric spaces and fractals. These Sobolev spaces include the well-known Hajfasz-Sobolev spaces as specialmodels.The author establishes varions chaaracterizations of(sharp)maximal functions for these spaces.Asapplications,the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces.Moreover;some embedding theorems are also given.     

Fixed point theorems for Ćirić-type strong almost contractions on partial metric spaces

In the present paper we prove some fixed point theorems for ?iri?-type strong almost contractions on partial metric spaces. We also give an illustrative example.     

Weak martingale Hardy spaces and weak atomic decompositions

In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms. They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory. And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved. With the help of the weak atomic decompositions of martingale, a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given. Using the sufficient condition, we obtain a series of martingale inequalities with respect to the weak Lp-norm, the inequalities of weak (p ,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces. These inequalities are the weak versions of the basic inequalities in the classical martingale Hp-theory.