Analysis Mathematica最新文献

We prove that the function (g(x)= 1 / ( 1 - cos(x) )) is completely monotonic on ((0,pi]) and absolutely monotonic on ([pi, 2pi)), and we determine the best possible bounds (lambda_n) and (mu_n) such that the inequalities

and

hold for all (x,yin (0,pi)) with (x+yleq pi).

The main purpose of this paper is to study the Bishop-Phelps-Bollobás property for operators on (c_0)-sum of Euclidean spaces. We show that the pair ( (c_0(bigoplus^{infty}_{k=1}ell^{k}_{2} ),Y)) has the Bishop-Phelps-Bollobás property for operators (shortly BPBp for operators) whenever (Y) is a uniformly convex Banach space.

In this paper, we study Riesz-Fejér inequality, comparative growth of integral means and boundary behavior for solutions of the (alpha)-harmonic equation in the unit disk (mathbb{D}). For (alpha>max{-1,-frac{2}{p}}) (alpha geq 0) and (1<p<infty), we obtain a Riesz-Fejér inequality for functions in the real kernel (alpha)-harmonic Hardy space consisting of solutions (u) of the (alpha)-harmonic equation in (mathbb{D}) with uniformly bounded integral mean (M_{p}(r, u)) with respect to (rin(0,1)). Furthermore, for (1leq p<qleqinfty), we estimate the growth of (M_{q}(r,u)) if the growth of (M_{p}(r,u)) is known. Moreover, we consider the boundary behavior of real kernel (alpha)-Poisson integrals in (mathbb{D}), where (alpha>-1). Our results generalize the related previous results.

For (alpha in (0,infty)), let (mathcal{B}_{mathcal{H},Omega}(alpha)) denote the class of (alpha)-Bloch mappings on a proper simply connected domain (Omega subseteq mathbb{C}). In this article, we introduce the class (mathcal{B}^{*}_{mathcal{H},Omega}(alpha)) of harmonic (alpha)-Bloch-type mappings on a proper simply connected domain (Omega subseteq mathbb{C}) and study several interesting properties of the classes (mathcal{B}_{mathcal{H},Omega}(alpha)) and (mathcal{B}^{*}_{mathcal{H},Omega}(alpha)) when (Omega) is proper simply connected domain and the shifted disk (Omega_{gamma}) containing (mathbb{D}), where

and (0 leq gamma <1). For (f in mathcal{B}_{mathcal{H},Omega}(alpha)) (respectively (mathcal{B}^{*}_{mathcal{H},Omega}(alpha))) of the form (f(z)=h(z) + overline{g(z)}=sum_{n=0}^{infty}a_nz^n + overline{sum_{n=1}^{infty}b_nz^n}) in (mathbb{D}) with Bloch norm ( lVert f rVert _{mathcal{H},Omega, alpha} leq 1) (respectively ( lVert f rVert ^{*}_{mathcal{H},Omega, alpha} leq 1)), we define the Bloch–Bohr radius for the class (mathcal{B}_{mathcal{H},Omega}(alpha)) (respectively (mathcal{B}^{*}_{mathcal{H},Omega}(alpha))) to be the largest radius (r_{Omega,alpha} in (0,1)) such that (sum_{n=0}^{infty}(|a_n|+|b_{n}|) r^nleq 1) for (r leq r_{Omega, alpha}) and for all (f in mathcal{B}_{mathcal{H},Omega}(alpha)) (respectively (mathcal{B}^{*}_{mathcal{H},Omega}(alpha))). We also investigate Bloch–Bohr radius for the classes (mathcal{B}_{mathcal{H},Omega}(alpha)) and (mathcal{B}^{*}_{mathcal{H},Omega}(alpha)) on simply connected domain (Omega) containing (mathbb{D}).

In this paper, we give a result on finiteness of meromorphic mappings from (mathbb C^m) into (mathbb P^n(mathbb C)) sharing hyperplanes in general position with truncated multiplicities to level (n). In our result, the number of shared hyperplanes is just (2n) instead of (2n+1) or (2n+2) as in the previous results, but the number of involving meromorphic mappings still does not exceed 2.

Let (T_{alpha}) be an (m)-linear fractional Calderón–Zygmund operator with kernel of mild regularity, and (vec{b} =(b_{1},b_{2} ,ldots,b_{m})) be a collection of locally integrable functions. In this paper, the main purpose is to establish some estimates for the mapping property of the multilinear commutators ( T_{{alpha,Sigma vec{b}}}) in the context of the variable exponent function spaces. The key tools used are the Fourier series and the pointwise estimates involving the sharp maximal operator of the multilinear commutator and certain associated maximal operators.

In this paper we consider the discrete Laplacian acting on1-forms and we study its spectrum relative to the spectrum of the 0-form Laplacian.We show that the nonzero spectrum can coincide for these Laplacians withthe same nature. We examine the characteristics of 0-spectrum of the 1-formLaplacian compared to the cycles of graphs.

We consider random Dirichlet series (f(s)=sum_{n=1}^{infty} varepsilon_n a_n e^{-lambda_{n} s}), with (a_n) complex numbers, (lambda_n geq 0), increasing to (infty) , and otherwise arbitrary; and with ((varepsilon_n)) a Rademacher sequence of random variables. We study their almost sure convergence on the critical line of convergence({ text{Re},, s=sigma_{c}(f)}.)When (lambda_n=n) (periodic case), a well-known sufficient condition on the coefficients a_n ensuring almost sure uniform convergence on ([0,2pi] ) (equivalently uniform convergence on (mathbb{R})) has been given by Salem and Zygmund, who made strong use of Bernstein's inequality. When ((lambda_n)) is arbitrary (non-periodic case), one must distinguish between uniform convergence on compact subsets of (mathbb{R}) (local convergence) and uniform convergence on (mathbb{R}). We extend Salem–Zygmund's theorem to general random Dirichlet series in this non-periodic case. Our main tools are a simple “local” Bernstein's inequality, and P. Lévy's symmetry principle.

We summarize some results as well as we prove some new results about the Orlicz–Lorentz–Karamata spaces and martingale Hardy Orlicz–Lorentz–Karamata spaces. More precisely, Doob's maximal inequality for submartingales and Burkholder–Davis–Gundy inequality are presented. We also show some fundamental martingale inequalities and modular inequalities. Additionally, based on atomic decompositions, duality theorems and fractional integral operators are discussed. As applications in Fourier analysis, we consider the Walsh–Fourier series on Orlicz–Lorentz–Karamata spaces. The dyadic maximal operators on martingale Hardy Orlicz–Lorentz–Karamata spaces are presented. The boundedness of maximal Fejér operator is proved, which further implies some convergence results of the Fejér means.