Let h(y) be a bounded radial function and Ω (y) an H function on the unit sphere satisfying the cancelation condition. Then the Marcinkiewicz integral operator μΩ related to the Littlewood-Paley g−function is defined by

The Clarkson-McLeod solutions of the fourth Painlevé equation behave like κDα−122(2x) as x→+∞, where κ is some real constant and Dα−12(x) parabolic cylinder function. Using Deift-Zhou nonlinear steepest descent method, we derive asymptotic behaviors for this class x→−∞. This completes a proof Clarkson McLeod's conjecture on asymptotics family solutions. total integrals approximations σ-form are...

Abstract We prove that the asymptotics of ergodic integrals along an invariant foliation a toral Anosov diffeomorphism, or pseudo-Anosov diffeomorphism on compact orientable surface higher genus, is determined (up to logarithmic error) by action cohomology surface. As consequence our argument and results Giulietti Liverani [Parabolic dynamics anisotropic Banach spaces. J. Eur. Math. Soc. (JEMS)...

Geodetic and meteorological data, collected via satellites for example, are genuinely scattered, and not confined to any special set of points. Even so, known quadrature formulas used in numerically computing integrals involving such data have had restrictions either on the sites (points) used or, more significantly, on the number of sites required. Here, for the unit sphere embedded in Rq, we ...

The continuity for some multilinear operators generated by certain integral operators and Lipschitz functions on some Hardy and Herz-type spaces are obtained. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.

The purpose of this paper is to study the endpoint boundedness properties of some multilinear operators related to certain integral operators on Herz and Herz type Hardy Spaces. The operators include Littlewood-Paley operator and Marcinkiewicz operator.

Error estimates are derived for a class of Galerkin methods for a quasilinear parabolic equation. In these Galerkin methods, both continuous and discrete in time, the nonlinear coefficient in the differential equation is interpolated into a finite-dimensional function space in order to compute the integrals involved. Asymptotic error estimates of optimal order are produced. Introduction. In ord...

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.