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Analysis in Theory and Applications

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ISSN (Print) 1573-8175 - ISSN (Online) 1672-4070
Published by Springer-Verlag

[2216 journals]

Boundedness of commutators for Marcinkiewicz integrals on weighted Herz-type Hardy spaces
- Abstract: In this paper, the authors study the boundedness of the operator µ Ω b , the commutator generated by a function b ∈ Lip β (R n )(0 < β < 1) and the Marcinkiewicz integral µΩ on weighted Herz-type Hardy spaces.
  PubDate: 2011-12-01
A simple proof of the chaoticity of shift map under a new definition of chaos
- Abstract: Recently, Du has given a new strong definition of chaos by using the shift map. In this paper, we give a proof of the main theorem by constructing a dense uncountable invariant subset of the symbol space Σ2 containing transitive points in a simpler way with the help of a different metric. We also provide two examples, which support this new definition.
  PubDate: 2011-12-01
The boundedness of Toeplitz-type Operators on vanishing-morrey spaces
- Abstract: In this note, we prove that the Toeplitz-type Operator Θ α b generated by the generalized fractional integral, Calderón-Zygmund operator and VMO funtion is bounded from L p,λ (R n ) to L q,µ(R n ). We also show that under some conditions Θ α b f ∈ VL q, µ(B R ), the vanishing-Morrey space.
  PubDate: 2011-12-01
A theoretical framework for the calculation of Hausdorff measure — Self-similar set satisfying OSC
- Abstract: A theoretical framework for the calculation of Hausdorff measure of self-similar sets satisfying OSC has been established.
  PubDate: 2011-12-01
Some results on topical functions and upward sets
- Abstract: The purpose of this paper is to introduce and discuss the concept of topical functions on upward sets. We give characterizations of topical functions in terms of upward sets.
  PubDate: 2011-12-01
Almost homomorphisms between unital C*-algebras: A fixed point approach
- Abstract: Let A,B be two unital C*-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h: A → B which satisfies h(2 n uy)= h(2 n u)h(y) for all u ∈ U(A), all y ∈ A, and all n=0,1,2, …, is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of *-homomorphisms on unital C*-algebras.
  PubDate: 2011-12-01
Some integral inequalities for the polar derivative of a polynomial
- Abstract: If P(z) is a polynomial of degree n which does not vanish in z < 1, then it is recently proved by Rather [Jour. Ineq. Pure and Appl. Math., 9 (2008), Issue 4, Art. 103] that for every γ> 0 and every real or complex number α with α ≥ 1, $\begin{gathered} \left\{ {\int_0^{2\pi } {\left {D_\alpha P(e^{i\theta } )} \right ^\gamma d\theta } } \right\}^{{1 \mathord{\left/ {\vphantom {1 \gamma }} \right. \kern-\nulldelimiterspace} \gamma }} \leqslant n( \alpha + 1)C_\gamma \left\{ {\int_0^{2\pi } {\left {P(e^{i\theta } )} \right ^\gamma d\theta } } \right\}^{{1 \mathord{\left/ {\vphantom {1 \gamma }} \right. \kern-\nulldelimiterspace} \gamma }} , \hfill \\ C_\gamma \left\{ {\frac{1} {{2\pi }}\int_0^{2\pi } {\left {1 + e^{i\beta } } \right ^\gamma d\beta } } \right\}^{ - {1 \mathord{\left/ {\vphantom {1 \gamma }} \right. \kern-\nulldelimiterspace} \gamma }} \hfill \\ \end{gathered} $ where D α P(z) denotes the polar derivative of P(z) with respect to α. In this paper we prove a result which not only provides a refinement of the above inequality but also gives a result of Aziz and Dawood [J. Approx. Theory, 54 (1988), 306–313] as a special case.
  PubDate: 2011-12-01
Harmonic mappings of the hexagasket to the circle
- Abstract: Harmonic mappings from the hexagasket to the circle are described in terms of boundary values and topological data. Explicit formulas are also given for the energy of the mapping. We have generalized the results in [10].
  PubDate: 2011-12-01
On double sine and cosine transforms, Lipschitz and Zygmund classes
- Abstract: We consider complex-valued functions f ∈ L 1(R + 2 ), where R +:= [0,∞), and prove sufficient conditions under which the double sine Fourier transform $\hat f_{ss} $ and the double cosine Fourier transform $\hat f_{cc} $ belong to one of the two-dimensional Lipschitz classes Lip(α, β) for some 0 < α, β ≤ 1; or to one of the Zygmund classes Zyg(α, β) for some 0 < α, β ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L 1(R + 2 ).
  PubDate: 2011-12-01
Measures of weak noncompactness and fixed point theory for 1-set weakly contractive operators on unbounded domains
- Abstract: The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F(x) =αx (α ≥ 1) for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for the nonlinear operator equation F(x) = αx (α ≥ 1) for such class of operators. As consequences, the main results generalize and improve the relevant results, which are obtained by O’Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive (µ-nonexpansive) and weakly semi-closed operators at the origin and their generalizations. The main condition in our results is formulated in terms of axiomatic measures of weak compactness.
  PubDate: 2011-09-01
On convergence of general Gamma type operators
- Abstract: The present paper deals with the new type of Gamma operators, here we estimate the rate of pointwise convergence of these new Gamma type operators M n,k for functions of bounded variation, by using some techniques of probability theory.
  PubDate: 2011-09-01
A new BLO estimate for maximal singular integral operators
- Abstract: In this paper, we extend Hu and Zhang’s results in [2] to different case.
  PubDate: 2011-09-01
Weighted approximation of r-monotone functions on the real line by Bernstein operators
- Abstract: In this paper, we give error estimates for the weighted approximation of r-monotone functions on the real line with Freud weights by Bernstein-type operators.
  PubDate: 2011-09-01
Uniform meyer solution to the three dimensional cauchy problem for laplace equation
- Abstract: We consider the three dimensional Cauchy problem for the Laplace equation $\left\{ \begin{gathered} u_{xx} (x,y,z) + u_{yy} (x,y,z) + u_{zz} (x,y,z) = 0,x \in R,y \in R,0 < z \leqslant 1, \hfill \\ u(x,y,0) = g(x,y),x \in R,y \in R, \hfill \\ u_z (x,y,0) = 0,x \in R,y \in R, \hfill \\ \end{gathered} \right. $ where the data is given at z = 0 and a solution is sought in the region x,y ∈ R,0 < z < 1. The problem is ill-posed, the solution (if it exists) doesn’t depend continuously on the initial data. Using Galerkin method and Meyer wavelets, we get the uniform stable wavelet approximate solution. Furthermore, we shall give a recipe for choosing the coarse level resolution.
  PubDate: 2011-09-01
Approximation and shape-preserving properties of q-Stancu operator
- Abstract: We introduce the definition of q-Stancu operator and investigate its approximation and shape-preserving property. With the help of the sign changes of f (x) and L n = f (f,q;x) the shape-preserving property of q-Stancu operator is obtained.
  PubDate: 2011-09-01
Some applications of BP-theorem in approximation theory
- Abstract: In this paper we apply Bishop-Phelps property to show that if X is a Banach space and G ⊆ X is the maximal subspace so that G ⊥ = {x* ∈ X* x*(y)=0; Åy ∈ G} is an L-summand in X*, then L 1(Ω,G) is contained in a maximal proximinal subspace of L 1(Ω,X).
  PubDate: 2011-09-01
A note on H _w ^p -boundedness of Riesz transforms and θ -Calderón-Zygmund operators through molecular characterization
- Abstract: Let 0 < p ≤ 1 and w in the Muckenhoupt class A 1. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and Yang[11] established that the Riesz transforms R j , j = 1,2, …,n, are bounded on H w p (R n ). In this note we extend this to the general case of weight w in the Muckenhoupt class A ∞ through molecular characterization. One difficulty, which has not been taken care in [11], consists in passing from atoms to all functions in H w p (R n ). Furthermore, the H w p -boundedness of θ-Calderón-Zygmund operators are also given through molecular characterization and atomic decomposition.
  PubDate: 2011-09-01
Bmo boundedness for banach space valued singular integrals
- Abstract: In this paper, we consider a class of Banach space valued singular integrals. The L p boundedness of these operators has already been obtained. We shall discuss their boundedness from BMO to BMO. As applications, we get BMO boundedness for the classic g-function and the Marcinkiewicz integral. Some known results are improved.
  PubDate: 2011-09-01
Bounds for commutators of multilinear fractional integral operators with homogeneous kernels
- Abstract: We will show bounds for commutators of multilinear fractional integral operators with some homogeneous kernels.
  PubDate: 2011-06-01
Hybrid fixed point result for lipschitz homomorphisms on quasi-Banach algebras
- Abstract: We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.
  PubDate: 2011-06-01