On Function Spaces of Variable Order of Differentiation.
On global approximation properties of abstract integral operators in Orlicz spaces and applications.
On integral operators with operator-valued kernels.
On Integral Representations and a priori Lipschitz Estimates for the Canonical Solution of the ...-Equation.
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 Mikusinski's perators of fractional integration
On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes
Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.In this paper the multi-dimensional analog of the Gillis-Weiss random walk model is studied. The convergence of this random walk to a fractional diffusion process governed by a symmetric operator defined as a hypersingular integral or the inverse of the Riesz potential in the sense of distributions is proved.* Supported by German Academic Exchange Service (DAAD).
On multilinear singular integrals of Calderón-Zygmund type.
A variety of results regarding multilinear singular Calderón-Zygmund integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur's test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators. A maximal...
On nonintegrality of functions of some integral and partially integral operators.
On one class of operators associated with differential equations of fractional order.
On operators induced by weakly 2-singular kernels
On oscillatory integral operators with folding canonical relations
Sharp estimates are proven for oscillatory integrals with phase functions Φ(x,y), (x,y) ∈ X × Y, under the assumption that the canonical relation projects to T*X and T*Y with fold singularities.
On Pseudo-Differential Operators and Smoothness of Special Lie-Group Representations.
On random evolutions induced by countable state space Markov chains
On realizations related to Weyl operators.
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 analytical index formulas related to operator-valued symbols.
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 spectra of geometric operators on open manifolds and differentiable groupoids.