Authors:Bai Linglan; He Jianxun Pages: 48 - 62 Abstract: Abstract Let X=R + n ×R denote the underlying manifold of polyradial functions on the Heisenberg group Hn. We construct a generalized translation on X=R + n ×R, and establish the Plancherel formula on L2(X, dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X. PubDate: 2013-09-18 DOI: 10.1007/bf02845274 Issue No:Vol. 18, No. 4 (2013)

Authors:A. Al-Shuaibi Pages: 58 - 65 Abstract: Abstract A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum $$f\left( t \right) \cong \sum\limits_{b \approx 0}^N {b_k \left( \alpha \right)\frac{{d^h G\left( x \right)}} {{dx^h }}}$$ , where bk(a) are precalculated and tabulated regularization coefficients, G(x)=ex(ex) and g(x) is the given Laplace transform of f(t). Error bounds together with an algorithm to calculate the coefficients bk (a) and some examples are also discussed. Perturbed data problems are not included. PubDate: 2013-09-18 DOI: 10.1007/bf02836897 Issue No:Vol. 13, No. 1 (2013)

Authors:H. Hosni; M. R. Haddai; H. Mazaheri Pages: 301 - 308 Abstract: 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 DOI: 10.1007/s10496-011-0301-6 Issue No:Vol. 27, No. 4 (2011)

Authors:Xiaoniu Cao; Dongxiang Chen Pages: 309 - 319 Abstract: 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 DOI: 10.1007/s10496-011-0309-y Issue No:Vol. 27, No. 4 (2011)

Authors:M. Eshaghi Gordji; S. Kaboli Gharetapeh; M. Bidkham; T. Karimi; M. Aghaei Pages: 320 - 331 Abstract: 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 DOI: 10.1007/s10496-011-0320-3 Issue No:Vol. 27, No. 4 (2011)

Authors:Indranil Bhaumik; Binayak S. Choudhury; Basudeb Mukhopadhyay Pages: 332 - 339 Abstract: 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 DOI: 10.1007/s10496-011-0332-z Issue No:Vol. 27, No. 4 (2011)

Authors:Abdullah Mir; Sajad Amin Baba Pages: 340 - 350 Abstract: 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 DOI: 10.1007/s10496-011-0340-z Issue No:Vol. 27, No. 4 (2011)

Authors:Vanda Fülöp; Ferenc Móricaz Pages: 351 - 364 Abstract: 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 DOI: 10.1007/s10496-011-0351-9 Issue No:Vol. 27, No. 4 (2011)

Authors:Cuilan Wu Pages: 365 - 376 Abstract: 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 DOI: 10.1007/s10496-011-0364-4 Issue No:Vol. 27, No. 4 (2011)

Authors:Donglei Tang Pages: 377 - 386 Abstract: 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 DOI: 10.1007/s10496-011-0377-z Issue No:Vol. 27, No. 4 (2011)

Authors:Zuoling Zhou; Li Feng Pages: 387 - 398 Abstract: Abstract A theoretical framework for the calculation of Hausdorff measure of self-similar sets satisfying OSC has been established. PubDate: 2011-12-01 DOI: 10.1007/s10496-011-0387-x Issue No:Vol. 27, No. 4 (2011)

Authors:Lianying Yun; Rongwei Wang Pages: 201 - 210 Abstract: 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 DOI: 10.1007/s10496-011-0201-9 Issue No:Vol. 27, No. 3 (2011)

Authors:Qiquan Fang; Xianliang Shi Pages: 211 - 219 Abstract: Abstract In this paper, we extend Hu and Zhang’s results in [2] to different case. PubDate: 2011-09-01 DOI: 10.1007/s10496-011-0211-7 Issue No:Vol. 27, No. 3 (2011)

Authors:I. Sadeqi; R. Zarghami Pages: 220 - 223 Abstract: 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 DOI: 10.1007/s10496-011-0220-6 Issue No:Vol. 27, No. 3 (2011)

Authors:Shaoyuan Xu; Afif Ben Amar Pages: 224 - 238 Abstract: 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 DOI: 10.1007/s10496-011-0224-2 Issue No:Vol. 27, No. 3 (2011)

Authors:Laiyi Zhu; Xiaojie Zhu; Xing Liu Pages: 239 - 250 Abstract: 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 DOI: 10.1007/s10496-011-0239-8 Issue No:Vol. 27, No. 3 (2011)

Authors:Luong Dang Ky Pages: 251 - 264 Abstract: 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 DOI: 10.1007/s10496-011-0251-z Issue No:Vol. 27, No. 3 (2011)

Authors:Jinru Wang; Weifang Wang Pages: 265 - 277 Abstract: 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 DOI: 10.1007/s10496-011-0265-6 Issue No:Vol. 27, No. 3 (2011)

Authors:Chunjie Zhang Pages: 278 - 287 Abstract: 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 DOI: 10.1007/s10496-011-0278-1 Issue No:Vol. 27, No. 3 (2011)

Authors:Harun Karsli Pages: 288 - 300 Abstract: 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 DOI: 10.1007/s10496-011-0288-z Issue No:Vol. 27, No. 3 (2011)