[PDF] Top 20 Approximation of Functions by Singular Integrals

... of function . Note that the function D 3 (5) was firstly introduced in [14]. If f(5) is positive function which is monotone increasing on interval (0, +∞) , then "Dg h = "Dg h ( ) denotes the set of all ... See full document

... in approximation by complex Pi- card, Poisson-Cauchy, and Gauss-Weierstrass singular integrals with Jackson-type rate, having the quality of preservation of some properties in geometric function ... See full document

... This paper is devoted to investigating the boundedness of the oscillation and variation operators for the commutators generated by Calderón-Zygmund singular integrals with Lipschitz functions in the ... See full document

... The oscillation and variation for some families of operators have been studied by many authors on probability, ergodic theory, and harmonic analysis; see [–]. Recently, some authors [–] researched the weighted ... See full document

... If we choose p = 2 in (2.28), we have Laplace equation Δu = 0 for functions. Hence, the Equations (2.28), (2.29) and the Δu = 0 are the special cases of the non-homoge- neous A-harmonic equation (1.1). Therefore, ... See full document

... multiple singular integrals with rough kernels on product spaces ℝ n × ℝ m ( n, m ≥ ...multiple singular integral operators are bounded on L p (ℝ n × ℝ m ) for the kernel functions: Ω Î L (log ... See full document

... Zygmund singular integral operators has attracted more and more attention, which orig- inated from the work of Coifman and Meyer [], and it systematically was studied by Grafakos and Torres [, ...Zygmund ... See full document

... many functions especially having a singular ...such singular integrals by considering unequal sub-divisions of an interval which again excludes the functional value at x 0 ... See full document

... the solution of the matrix equation, can be obtained analyti- cally (see Fichte et al., 2004). The calculations resulting from the analytical approach are discussed in detail in Fichte (@). Once the values of these ... See full document

... nonlinear singular integral operators [, ], a family of nonlinear m-singular integral operators [], Fejer-Type singular integrals [], moment type operators [], a family of nonlinear ... See full document

... Subsequently, Ying and Chen [] (resp., Al-Salman et al. []) extended the result of [] to the multiple singular integrals along polynomial curves (resp., associated with poly- nomial mappings). We also ... See full document

... Ziesler, “Singular Integrals and Maximal Functions Associated to Surfaces of Revolution,” Bulletin London Mathematical Society, Vol.. Yang, “Rough Singular Integrals Associated to Surfac[r] ... See full document

... In this article we study the degree of L p -approximation (1 ≤ p ≤ +∞) to the unit, by univariate and multivariate variants of the Jackson-type generalizations of Picard, Gauss–Weierstra[r] ... See full document

... Optimal with respect to order quadrature rule for the evaluation integral as (1.27) on Hölder and Sobolev classes of functions was constructed in [26]. Later asymptotically optimal and optimal with respect to ... See full document

... for functions whose boundary measures are absolutely ...of functions in the disc. The bound is achieved for functions whose boundary measures, for example, are purely ... See full document

... These integrals are classified by the order of ...strongly singular. If p > 1 , the integral is called hyper-singular, see ...weakly singular if its value exists and continuous at the ... See full document

... In [1], M. D. Brue introduced the functional transform on the Feynman integral (1972). In [2], R. H. Cameron wrote the paper about the translation pathology of a Wiener space (1954). In [3] [4] [5], R. H. Cameron and W. ... See full document

... Abstract. Integrals of logarithmic and hypergeometric functions are intrin- sically connected with Euler ...of integrals of logarithmic, hypergeometric functions and the Lerch phi transcendent ... See full document

... INTEGRALS OF OPERATOR-VALUED FUNCTIONS has separated variables, say ht,x ordinary convolution h *h.. of the two factors.[r] ... See full document

... Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Inventiones Mathematicae 84 1986, no.. Pan, L p estimates for singular integrals associated to [r] ... See full document