About the Lp-Boundedness of Integral Operators with Kernels of the Form K1 (x-y)K2(x+y).
Absolute continuity for elliptic-caloric measures
A Carleson condition on the difference function for the coefficients of two elliptic-caloric operators is shown to give absolute continuity of one measure with respect to the other on the lateral boundary. The elliptic operators can have time dependent coefficients and only one of them is assumed to have a measure which is doubling. This theorem is an extension of a result of B. Dahlberg [4] on absolute continuity for elliptic measures to the case of the heat equation. The method of proof is an...
Absolute convergence of multiple Fourier integrals
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained. The results are given in terms of integrability of the function and its partial derivatives, each with a different p. These p are subject to certain relations known earlier only for some particular cases. Sharpness and applications of the results obtained are also discussed.
Adaptive Deterministic Dyadic Grids on Spaces of Homogeneous Type
In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic grids, specifically adapted to a given combinatorial situation. This method is used to estimate vector-valued operators rearranging martingale difference sequences such as the Haar system.
Addendum to a paper "On singular integrals"
Algebras of Special Singular Integrals over Local Fields.
Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment
Bellow and Calderón proved that the sequence of convolution powers converges a.e, when is a strictly aperiodic probability measure on such that the expectation is zero, , and the second moment is finite, . In this paper we extend this result to cases where .
Almost everywhere convergence of the spherical partial Fourier integrals for radial functions.
Almost Everywhere Convergence of the Spherical Partial Sums for Radial Functions.
Alternative characterisations of Lorentz-Karamata spaces
We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.
An abstract version of Herz' imbedding theorem
An analytic solution to the Busemann-Petty problem on sections of convex bodies.
An Application of Littlewood-Paley Theory in Harmonie Analysis.
An application of the Fourier transform to optimization of continuous 2-D systems
This paper uses the theory of entire functions to study the linear quadratic optimization problem for a class of continuous 2D systems. We show that in some cases optimal control can be given by an analytical formula. A simple method is also proposed to find an approximate solution with preassigned accuracy. Some application to the 1D optimization problem is presented, too. The obtained results form a theoretical background for the design problem of optimal controllers for relevant processes.
An atomic theory of ergodic spaces
An Elementary Approach to Local Solvability for Constant Coefficient Partial Differential Equations.
An embedding relation for bounded mean oscillation on rectangles
In the two-parameter setting, we say a function belongs to the mean little BMO if its mean over any interval and with respect to any of the two variables has uniformly bounded mean oscillation. This space has been recently introduced by S. Pott and the present author in relation to the multiplier algebra of the product BMO of Chang-Fefferman. We prove that the Cotlar-Sadosky space of functions of bounded mean oscillation is a strict subspace of the mean little BMO.
An End Point Estimate for Maximal Commutators.
An endpoint estimate for some maximal operators.
An estimation for a family of oscillatory integrals
Let K be a Calderón-Zygmund kernel and P a real polynomial defined on ℝⁿ with P(0) = 0. We prove that convolution with Kexp(i/P) is continuous on L²(ℝⁿ) with bounds depending only on K, n and the degree of P, but not on the coefficients of P.