In this paper Lq → Lp boundedness of integral operator with operator-valued kernels is studied and main result is applied to convolution operators.

The Gaussian scale-space is a singular integral convolution operator with scaled Gaussian kernel. For a large class of singular integral convolution operators with differentiable kernels, a general method for constructing mother wavelets for continuous wavelet transforms is developed, and Calderón type inversion formulas, in both integral and semi-discrete forms, are derived for functions in L ...

Usually, the fast evaluation of a convolution integral R R f(y)g(x−y)dy requires that the functions f, g have a simple structure based on an equidistant grid in order to apply the fast Fourier transform. Here we discuss the efficient performance of the convolution of hp-functions in certain locally refined grids. More precisely, the convolution result is projected into some given hp-space (Gale...

is finite. The purpose of this paper is to provide a framework for proving inequalities of the form (1). The idea is to exploit the close relationship of the Fourier transform to the operation of convolution and then to apply techniques from the theory of positive integral operators. Although the convolution operators that arise are not necessarily positive, they are trivially majorized by posi...

Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.