The commutators of oscillatory singular integral operators with homogeneous kernel $\frac{{\Omega (x)}}{{\left| x \right|^n }}$ are studied, where Ω is homogeneous of degree zero, has mean value zero on the unit sphe...The commutators of oscillatory singular integral operators with homogeneous kernel $\frac{{\Omega (x)}}{{\left| x \right|^n }}$ are studied, where Ω is homogeneous of degree zero, has mean value zero on the unit sphere. It is proved that Ω∈L (logL)K+1(Sn-1) is a sufficient condition under which the k-th order commutator is bounded on L2(Rn).展开更多
This is a short survey on osicllatory integral operators. We summarize the main development and managing techniques of the field, and give some open problems and main references in the end.
In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator; and using this, t...In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator; and using this, the authors obtain the weightd inequalies for a wide class of sublinear singular operators defined onR n which include the Calderón-Zygmund operators as special cases. The fractional versions of these results are also given.展开更多
It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have ans...It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have answered the question proposed in [1].展开更多
Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they ar...Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they are shift-invariant both in space (or time) and in phase. This result is then applied to characterize dual frames and bi-orthogonal Riesz bases of L2.展开更多
The concern of this paper is to study local approximation properties of the Bernstein-Durrmeyer operators Mn. We derive the complete asymptotic expansion of the operators Mn and their derivatives as n tends to infinit...The concern of this paper is to study local approximation properties of the Bernstein-Durrmeyer operators Mn. We derive the complete asymptotic expansion of the operators Mn and their derivatives as n tends to infinity. It turns out that the appropriate representation is a series of reciprocal factorials. All coefficients are calculated explicitly in a very concise form. Our main theorem contains several earlier partial results as special cases. Finally, we obtain a Voronovskaja-type formula for simultaneous approximation by linear combinations of Mn,展开更多
In this paper, we establish two multiplier theorems for Herz type Hardy spaces, and as an application, we discuss the boundedness of pseudo-differential operators in these spaces.
In this note a new generalized version of the classical Landau-Kolmogorov and Stein inequalities is established on a convolution class of periodic functions with a NCVD kernel. On this basis some sets of optimal subsp...In this note a new generalized version of the classical Landau-Kolmogorov and Stein inequalities is established on a convolution class of periodic functions with a NCVD kernel. On this basis some sets of optimal subspaces for the 2n-dimensional Kolgmogorov width of such function class are identified.展开更多
This paper deals with Kolmogorov criterion for best uniform coapproximation and strongly unique best uniform coapproximation. Some relations between best uniform approximation and best uniform coapproximation are obta...This paper deals with Kolmogorov criterion for best uniform coapproximation and strongly unique best uniform coapproximation. Some relations between best uniform approximation and best uniform coapproximation are obtained. Some equalities and best uniform coapproximation are connected.展开更多
In this paper, we systematically study a class of waves. We then de fine Hardy type spaces by conjugate systems for this class of waves, and study their properties. In particular, we show that they extend some class o...In this paper, we systematically study a class of waves. We then de fine Hardy type spaces by conjugate systems for this class of waves, and study their properties. In particular, we show that they extend some class of Lp estimates for the wave equation.展开更多
In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for gener...In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights.展开更多
In this paper the author presents a method for the numerical solution of a 2-D Cauchy principal value of the formwhere S is a domain with a continuous boundary. By usmg polar coordinates, the integral is reduced to th...In this paper the author presents a method for the numerical solution of a 2-D Cauchy principal value of the formwhere S is a domain with a continuous boundary. By usmg polar coordinates, the integral is reduced to the formwhere denotes the finite-part of the integral. We construct the relative product rule based onquasi-interpolating splines.Convergence results are proved and numerical examples are given.展开更多
In this paper the concept of positive definite bilinear matrix moment functional. acting on the space of all the matrix valued continuous functions defined on a bounded interval [a,b], is introduced. The best approxim...In this paper the concept of positive definite bilinear matrix moment functional. acting on the space of all the matrix valued continuous functions defined on a bounded interval [a,b], is introduced. The best approximation matrix problem with respect to such a functional is solved in terms of matrix Fourier series. Basic properties of matrix Fourier series such as the Kiemann -Lebesgue matrix property and the bessel-parseval matrix inequality are proved. The concept of total set vjith respect to a positive definite matrix functional is introduced , and the totallity of an orthonormal sequence of matrix polynomials with respect to the functional, is established.展开更多
We present a parallel iterative algorithm to find the shortest distance projection of a given point onto the intersection of a finite number of closed convex sets in a real Hilbert space ; the number of sets used at e...We present a parallel iterative algorithm to find the shortest distance projection of a given point onto the intersection of a finite number of closed convex sets in a real Hilbert space ; the number of sets used at each iteration stept corresponding to the number of available processors, may be smaller than the total number of sets. The relaxation coefficient at each iteration step is determined by a geometrical condition in an associated Hilbert space, while for the weights mild conditions are given to assure norm convergence of the resulting sequence. These mild conditions leave enough flexibility to determine the weights more specifically in order to improve the speed of convergence.展开更多
文摘The commutators of oscillatory singular integral operators with homogeneous kernel $\frac{{\Omega (x)}}{{\left| x \right|^n }}$ are studied, where Ω is homogeneous of degree zero, has mean value zero on the unit sphere. It is proved that Ω∈L (logL)K+1(Sn-1) is a sufficient condition under which the k-th order commutator is bounded on L2(Rn).
文摘This is a short survey on osicllatory integral operators. We summarize the main development and managing techniques of the field, and give some open problems and main references in the end.
文摘In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator; and using this, the authors obtain the weightd inequalies for a wide class of sublinear singular operators defined onR n which include the Calderón-Zygmund operators as special cases. The fractional versions of these results are also given.
文摘It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have answered the question proposed in [1].
文摘Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they are shift-invariant both in space (or time) and in phase. This result is then applied to characterize dual frames and bi-orthogonal Riesz bases of L2.
文摘The concern of this paper is to study local approximation properties of the Bernstein-Durrmeyer operators Mn. We derive the complete asymptotic expansion of the operators Mn and their derivatives as n tends to infinity. It turns out that the appropriate representation is a series of reciprocal factorials. All coefficients are calculated explicitly in a very concise form. Our main theorem contains several earlier partial results as special cases. Finally, we obtain a Voronovskaja-type formula for simultaneous approximation by linear combinations of Mn,
文摘In this paper, we establish two multiplier theorems for Herz type Hardy spaces, and as an application, we discuss the boundedness of pseudo-differential operators in these spaces.
文摘In this note a new generalized version of the classical Landau-Kolmogorov and Stein inequalities is established on a convolution class of periodic functions with a NCVD kernel. On this basis some sets of optimal subspaces for the 2n-dimensional Kolgmogorov width of such function class are identified.
文摘This paper deals with Kolmogorov criterion for best uniform coapproximation and strongly unique best uniform coapproximation. Some relations between best uniform approximation and best uniform coapproximation are obtained. Some equalities and best uniform coapproximation are connected.
文摘In this paper, we systematically study a class of waves. We then de fine Hardy type spaces by conjugate systems for this class of waves, and study their properties. In particular, we show that they extend some class of Lp estimates for the wave equation.
文摘In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights.
文摘In this paper the author presents a method for the numerical solution of a 2-D Cauchy principal value of the formwhere S is a domain with a continuous boundary. By usmg polar coordinates, the integral is reduced to the formwhere denotes the finite-part of the integral. We construct the relative product rule based onquasi-interpolating splines.Convergence results are proved and numerical examples are given.
文摘In this paper the concept of positive definite bilinear matrix moment functional. acting on the space of all the matrix valued continuous functions defined on a bounded interval [a,b], is introduced. The best approximation matrix problem with respect to such a functional is solved in terms of matrix Fourier series. Basic properties of matrix Fourier series such as the Kiemann -Lebesgue matrix property and the bessel-parseval matrix inequality are proved. The concept of total set vjith respect to a positive definite matrix functional is introduced , and the totallity of an orthonormal sequence of matrix polynomials with respect to the functional, is established.
文摘We present a parallel iterative algorithm to find the shortest distance projection of a given point onto the intersection of a finite number of closed convex sets in a real Hilbert space ; the number of sets used at each iteration stept corresponding to the number of available processors, may be smaller than the total number of sets. The relaxation coefficient at each iteration step is determined by a geometrical condition in an associated Hilbert space, while for the weights mild conditions are given to assure norm convergence of the resulting sequence. These mild conditions leave enough flexibility to determine the weights more specifically in order to improve the speed of convergence.
