On a class of operators on Orlicz spaces
On a new Hilbert-Hardy-type integral operator and applications.
On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball.
On an integral-type operator from Zygmund-type spaces to mixed-norm spaces on the unit ball.
On Continuity of Singular Integral Operators in Sobolev Spaces.
On convolution operators in the spaces of almost periodic functions and spaces.
On essential norm of the Neumann operator
One of the classical methods of solving the Dirichlet problem and the Neumann problem in is the method of integral equations. If we wish to use the Fredholm-Radon theory to solve the problem, it is useful to estimate the essential norm of the Neumann operator with respect to a norm on the space of continuous functions on the boundary of the domain investigated, where this norm is equivalent to the maximum norm. It is shown in the paper that under a deformation of the domain investigated by a diffeomorphism,...
On global approximation properties of abstract integral operators in Orlicz spaces and applications.
On integral operators with operator-valued kernels.
On limits of -norms of an integral operator
A recurrence relation for the computation of the -norms of an Hermitian Fredholm integral operator is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the -norms for the approximation of the spectral radius of this operator an a priori and an a posteriori bound for the error are obtained. Some properties of the a posteriori bound are discussed.
On nonintegrality of functions of some integral and partially integral operators.
On operators induced by weakly 2-singular kernels
On singular integrals of Calderón-type in Rn and BMO.
We prove Lp (and weighted Lp) bounds for singular integrals of the formp.v. ∫Rn E (A(x) - A(y) / |x - y|) (Ω(x - y) / |x - y|n) f(y) dy,where E(t) = cos t if Ω is odd, and E(t) = sin t if Ω is even, and where ∇ A ∈ BMO. Even in the case that Ω is smooth, the theory of singular integrals with rough kernels plays a key role in the proof. By standard techniques, the trigonometric function E can then be replaced by a large class of smooth functions F. Some related operators are also considered. As...
On solutions of integral equations with analytic kernels and rotations
We deal with a class of integral equations on the unit circle in the complex plane with a regular part and with rotations of the form (*) x(t) + a(t)(Tx)(t) = b(t), where and are of the form (3) below. We prove that under some assumptions on analytic continuation of the given functions, (*) is a singular integral equation for m odd and is a Fredholm equation for m even. Further, we prove that T is an algebraic operator with characteristic polynomial . By means of the Riemann boundary value...
On some structural properties of Banach function spaces and boundedness of certain integral operators
In this paper the notions of uniformly upper and uniformly lower -estimates for Banach function spaces are introduced. Further, the pair of Banach function spaces is characterized, where and satisfy uniformly a lower -estimate and uniformly an upper -estimate, respectively. The integral operator from into of the form is studied, where , , are prescribed functions under some local integrability conditions, the kernel is non-negative and is assumed to satisfy certain additional...
On the asymptotics of certain Wiener--Hopf-plus-Hankel determinants.
On the boundedness of Cauchy singular operator from the space to .
On the boundedness of fractional -maximal operators in the Lorentz spaces .
On the functions of one selfadjoint integral operator.
On the Hardy-type integral operators in Banach function spaces.
Characterization of the mapping properties such as boundedness, compactness, measure of non-compactness and estimates of the approximation numbers of Hardy-type integral operators in Banach function spaces are given.