The characters of supercuspidal representations as weighted orbital integrals

Weighted orbital integrals are the terms which occur on the geometric side of the trace formula. We shall investigate these distributions on ap-adic group. We shall evaluate the weighted orbital integral of a supercuspidal matrix coefficient as a multiple of the corresponding character. Supported in part by NSERC Operating Grant A3483.     

An equivalence for weighted integrals of an analytic function and ist derivative

In this paper we introduce the class of differentiable weights ω in the unit disc ?? such that where L is a positive constant. The main result in this paper asserts that if ω is one of these weights, then the equivalence holds for all 0 < p < ∞, 0 < q ≤ ∞and f an analytic function in ??. Our results improve others due to Aleman, Siskakis, and Stevi?. We also prove two results on harmonic conjugate functions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On weighted inequalities for singular integrals

In this note we consider singular integrals associated to Calderón-Zygmund kernels. We prove that if the kernel is supported in then the one-sided condition, , is a sufficient condition for the singular integral to be bounded in , , or from into weak- if . This one-sided condition becomes also necessary when we require the uniform boundedness of the singular integrals associated to the dilations of a kernel which is not identically zero in . The two-sided version of this result is also obtained: Muckenhoupts condition is necessary for the uniform boundedness of the singular integrals associated to the dilations of a general Calderón-Zygmund kernel which is not the function zero either in or in .

     

Sharp weighted inequalities for multilinear fractional maximal operators and fractional integrals

In this paper, we study weighted inequalities for multilinear fractional maximal operators and fractional integrals. We prove sharp weighted Lebesgue space estimates for both operators when the vector of weights belongs to . In addition we prove sharp two weight mixed estimates for multilinear operators in the spirit of the linear estimates given in 3 .     

Numerical evaluation of the two-dimensional partition of unity boundary integrals for Helmholtz problems

There has been considerable attention given in recent years to the problem of extending finite and boundary element-based analysis of Helmholtz problems to higher frequencies. One approach is the Partition of Unity Method, which has been applied successfully to boundary integral solutions of Helmholtz problems, providing significant accuracy benefits while simultaneously reducing the required number of degrees of freedom for a given accuracy. These benefits accrue at the cost of the requirement to perform some numerically intensive calculations in order to evaluate boundary integrals of highly oscillatory functions. In this paper we adapt the numerical steepest descent method to evaluate these integrals for two-dimensional problems. The approach is successful in reducing the computational effort for most integrals encountered. The paper includes some numerical features that are important for successful practical implementation of the algorithm.     

Convergence of weighted averages of relaxed projections

The convergence of the algorithm for solving convex feasibility problem is studied by the method of sequential averaged and relaxed projections. Some results of H. H. Bauschke and J. M. Borwein are generalized by introducing new methods. Examples illustrating these generalizations are given.     

A new method of numerical evaluation of singular integrals occurring in two-dimensional BIEM

A new quadrature rule for integrands having logarithmical singularities has been developed. This rule proved to be efficient especially in the context of the BIEM.     

Hyperbolic beta integrals

Hyperbolic beta integrals are analogues of Euler's beta integral in which the role of Euler's gamma function is taken over by Ruijsenaars’ hyperbolic gamma function. They may be viewed as -bibasic analogues of the beta integral in which the two bases q and q? are interrelated by modular inversion, and they entail q-analogues of the beta integral for |q|=1. The integrals under consideration are the hyperbolic analogues of the Ramanujan integral, the Askey-Wilson integral and the Nassrallah-Rahman integral. We show that the hyperbolic Nassrallah-Rahman integral is a formal limit case of Spiridonov's elliptic Nassrallah-Rahman integral.     

Asymptotic approximation of degenerate fiber integrals

We study asymptotics of fiber integrals depending on a large parameter. When the critical fiber is singular, full-asymptotic expansions are established in two different cases: local extremum and isolated real principal type singularities. The main coefficients are computed and invariantly expressed. In the most singular cases, it is shown that the leading term of the expansion is related to invariant measures on the spherical blow-up of the singularity. The results can be applied to certain degenerate oscillatory integrals which occur in spectral analysis and quantum mechanics.     

Boundedness of commutators for Marcinkiewicz integrals on weighted Herz-type Hardy spaces

In this paper,the authors study the boundedness of the operator μ b Ω,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.     

First-return integrals

Properties of first-return integrals of real functions defined on the unit interval are explored. In particular, first-return integrals are shown to be continuous but not absolutely continuous.     

Oscillation and variation inequalities for singular integrals and commutators on weighted Morrey spaces

This paper is devoted to investigating the bounded behaviors of the oscillation and variation operators for Calderón-Zygmund singular integrals and the corresponding commutators on the weighted Morrey spaces. We establish several criterions of boundedness, which are applied to obtain the corresponding bounds for the oscillation and variation operators of Hilbert transform, Hermitian Riesz transform and their commutators with BMO functions, or Lipschitz functions on weighted Morrey spaces.     

Fractional integrals on weighted Hardy spaces

In this paper, applying the atomic decomposition and molecular characterization of the real weighted Hardy spaces , we give the weighted boundedness of the homogeneous fractional integral operator from to , and from to .     

Multilinear singular and fractional integrals on weighted Hardy spaces

In this paper the boundedness properties of multilinear singular and fractional integrals on the weighted Hardy spaces are studied.     

Endpoint estimates for Marcinkiewicz integrals on weighted weak hardy spaces

In this paper, we obtain the(W H1ω, W L1ω) type estimate for the Marcinkiewicz integral and the(W H1 b,ω, W L1ω) type estimate for the commutator generated by a BMO function and the Marcinkiewicz integral, where the kernel satisfies a certain logarithmic type Lipschitz condition.     

On certain generalized families of unified elliptic-type integrals pertaining to Euler integrals and generating functions

Elliptic-type integrals have their importance and potential in certain problems in radiation physics and nuclear technology. A number of earlier works on the subject contains several interesting unifications and generalizations of some significant families of elliptic-type integrals. The present paper is intended to obtain certain new theorems on generating functions. The results obtained in this paper are of manifold generality and basic in nature. Beside deriving various known and new elliptic-type integrals and their generalizations these theorems can be used to evaluate various Euler-type integrals involving a number of generating functions.      

Two-weight norm inequalities for fractional maximal functions and fractional integral operators on weighted Morrey spaces

In this paper, we consider weighted norm inequalities for fractional maximal operators and fractional integral operators. For suitable weights, we prove the two-weight norm inequalities for both operators on weighted Morrey spaces.     

An undecidable property of definite integrals

We show that it is undecidable whether the definite contour multiple integral of an elementary meromorphic function is zero over an everywhere real analytic manifold on which it is analytic.

     

On the first-return integrals

Some pathological properties of the first-return integrals are explored. In particular it is proved that there exist Riemann improper integrable functions which are first-return recoverable almost everywhere, but not first-return integrable, with respect to each trajectory. It is also proved that the usual convergence theorems fail to be true for the first-return integrals.