Hlder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

In this paper we establish sharp H ¨older estimates of harmonic functions on a class of connected post critically finite(p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some well-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket,the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered.     

Approximation of Functions from the Hölder Class on a Half-Axis

Let (0 < < 1) be the Hölder class on the semi-axis [0,). We characterize the class by rates of approximation of its functions by entire functions of order 1/2 belonging to a special class (similarly to the classical JacksonBernstein theorem). Bibliography: 4 titles.     

The uv-Decomposition on a Class of D.C. Functions and Optimality Conditions

In this paper,the UV-theory and P-differential calculus are employed to study second-order ex-pansion of a class of D.C.functions and minimization problems.Under certain conditions,some properties ofthe U-Lagrangian,the second-order expansion of this class of functions along some trajectories are formulated.Some first and second order optimality conditions for the class of D.C.optimization problems are given.     

On a Class of Univalent Functions

A sharp coefficient estimate,distortion theorem and the radius of convexityare determined for the class R(α,β,A,B)of function f(z)=z+sum from n=2 to∞a_nz~n satisfyingthe condition|f’(z)-1/Bf’(z)-[B+(A-B)(1-α)]|<βfor someα,β(0≤α<1,0<β≤1)and-1≤A相似文献   

Boundary H¨older Estimates for a Class of Degenerate Elliptic Equations in Piecewise Smooth Domains*

In this paper, the authors will apply De Giorgi-Nash-Moser iteration to establish boundary H¨older estimates for a class of degenerate elliptic equations in piecewise C2smooth domains.     

On a Class of Additive Functions

ＯｎａＣｌａｓｓｏｆＡｄｄｉｔｉｖｅＦｕｎｃｔｉｏｎｓＺｈａｉｗｅｎｇｕａｎｇ（翟文广）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＳｈａｎｄｏｎｇＵｎｉｖ．，Ｊｉｎａｎ，Ｓｈｏｎｄｏｎｇ，２５０１Ｏ０）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＰａｎＣｈｅｎｇｂｉａｏＲｅｃｅｉ...     

Intrinsic Hölder Continuity of Harmonic Functions

We consider the stochastic differential equation (SDE) of the form

$$\begin{array}{@{}rcl@{}} \left\{\begin{array}{rcl} dX^ x(t) &=& \sigma(X(t-)) dL(t) \\ X^ x(0)&=&x,\quad x\in{\mathbb{R}}^ d, \end{array}\right. \end{array} $$

where \(\sigma :{\mathbb {R}}^ d\to {\mathbb {R}}^ d\) is globally Lipschitz continuous and L={L(t):t≥0} is a Lévy process. Under this condition on σ it is well known that the above problem has a unique solution X. Let \((\mathcal {P}_{t})_{t\ge 0}\) be the Markovian semigroup associated to X defined by \(\left ({\mathcal {P}}_{t} f\right ) (x) := \mathbb {E} \left [ f(X^ x(t))\right ]\), t≥0, \(x\in {\mathbb {R}}^{d}\), \(f\in \mathcal {B}_{b}({\mathbb {R}}^{d})\). Let B be a pseudo–differential operator characterized by its symbol q. Fix \(\rho \in \mathbb {R}\). In this article we investigate under which conditions on σ, L and q there exist two constants γ>0 and C>0 such that

$$\left| B {\mathcal{P}}_{t} u \right|_{H^{\rho}_{2}} \le C \, t^{-\gamma} \,\left| u \right|_{H^{\rho}_{2}}, \quad \forall u \in {H^{\rho}_{2}}(\mathbb{R}^{d} ),\, t>0. $$

     

The Comparison Theorems of Kolmogorov Type on a Convolution Class of Functions

ＴｈｅＣｏｍｐａｒｉｓｏｎ　ＴｈｅｏｒｅｍｓｏｆＫｏｌｍｏｇｏｒｏｖＴｙｐｅｏｎａＣｏｎｖｏｌｕｔｉｏｎＣｌａｓｓｏｆＦｕｎｃｔｉｏｎｓＣｈｅｎＤｉｒｏｎｇ（陈迪荣_（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＮｏｒｍａｌＵｎｉｖ?..     

On a Class of Fractal Interpolation Functions

ＯｎａＣｌａｓｏｆＦｒａｃｔａｌＩｎｔｅｒｐｏｌａｔｉｏｎＦｕｎｃｔｉｏｎｓＱｉａｎＸｉａｏｙｕａｎ（Ｉｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉｓ．，ＤａｌｉａｎＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ，１１６０２４）Ｋｅｙｗｏｒｄｓｉｔｅｒａｔｅｄｆｕｎ...     

Estimate of the Hölder Exponent Based on the $$epsilon$$ -Complexity of Continuous Functions

Mathematical Notes -     

Second-Order Expansion for a Class of Quasidifferentiable Functions

Suppose f, g:R~n→R are quasidifferentiable, and for an interval〔x,y〕:R~none has 0∈〈g(s)+g(s),y-x〉,s∈(x,y). Then there exists an η∈(x,y) suchthat     

Oscillation of Functions in the Hölder Class

Potential Analysis - We study the size of the set of points where the α-divided difference of a function in the Hölder class Λα is bounded below by a fixed positive constant....     

The Conditions of Equivalence of a Class Germs of C~∞ Functions on Banach Spaces

In this paper,we prove the converse of gem is right equivalent is also true in[1] and[2],obtain the necessary and sufficient conditions of equivalence of a class gems of C∞ function on Banach spaces.     

Second-Order Optimality Conditions for a Class of Quasidifferentiable Functions

Let f:R~n→R be continuously quasidifferentiable.Definition I The upper and lower.second-order d-directional derivativesof f at x are defined,respectively,by f”_+(x,v,d):(?)〈v_k+v_k-v,x_k-x〉/t_k~2,f”_(-)(x,v,d):(?)〈v_k+v_k-v,x_k-x〉/t_k~2,where(i)t_k>0,x_k→x;(ii)(x_k-x)/t_k→d;(iii)v_k+v_k→v,v_k∈(?)f(x_k),(?)∈(?)f(x_k).     

Construction and Dimension Analysis for a Class of Fractal Functions

In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, such as Bush type functions. These functions are fractal functions since their graphs are in general fractal sets. Under certain conditions, we investigate the fractal dimensions of the graphs of these functions, compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension. Meanwhile, the Holder continuity of such functions is also discussed.     

Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order

ABSTRACT

We consider a class of integrodifferential operators and their corresponding harmonic functions. Under mild assumptions on the family of jump measures we prove a priori estimates and establish Hölder continuity of bounded functions that are harmonic in a domain.     

Duality Theorems of Multiobjective Programming for a Class of Generalized Convex Functions

1.DefinitionsDefinition1.AfunctionalF(x)inthespaceVCE"issaidtobeasublinearfunctionalifforx,yeV,andor20,Inparticular,F(0)=0.Letop(x)beadifferentiablerealfunctiononasetCCEd.ForagivensublinearfunctionFandafunctionp:CxC-EIIp(x,u)/0(x/u),themoregeneralgeneralizedconvexfunctioncanbedefinedasthefollwing:Definition2.op(x)issaidtobe(F,p)--invarialltconvexfunctiononCifforxl,xZECDefinition3.op(x)issaidtobe(F,P)--invariantquasiconvexfunctiononCifforal,xZECthatis,Definition4.op(x)issaidtobe(F,…