Abstract The main purpose of this article is to establish some new characterizations the (variable) Lipschitz spaces in terms boundedness commutator multilinear fractional Calderón-Zygmund integral operators context variable exponent Lebesgue spaces. authors do so by applying techniques Fourier series and operator, as well pointwise estimates for commutators. key tool obtaining such a estimate ...

In this paper we apply a method of spectral theory of linear operators [10] to establish relations between the support of a function f on R with properties of its image Tf under a linear operator T : R → R. The classical approach uses analytic continuation of the image Tf into some complex domain (theorems of Paley-Wiener type [4, 5, 6, 7]), and therefore, could not apply to functions whose ima...

We discuss the form of the propagator U(t) for the timedependent Schrödinger equation on an asyptotically Euclidean, or, more generally, asymptotically conic, manifold with no trapped geodesics. In the asymptotically Euclidean case, if χ ∈ C∞ 0 , and with F denoting Fourier transform, F ◦ e 2/2tU(t)χ is a Fourier integral operator for t 6= 0. The canonical relation of this operator is a “sojour...

Abstract. Solution of some boundary value problems and initial problems in unique ball leads to the convergence and sumability problems of Fourier series of given function by eigenfunctions of Laplace operator on a sphere spherical harmonics. Such a series are called as Fourier-Laplace series on sphere. There are a number of works devoted investigation of these expansions in different topologie...

We study the microlocal properties of the geodesic X-ray transform X on a manifold with boundary allowing the presence of conjugate points. Assuming that there are no self-intersecting geodesics and all conjugate pairs are nonsingular we show that the normal operator N = X t ◦X can be decomposed as the sum of a pseudodifferential operator of order −1 and a sum of Fourier integral operators. We ...

some estimates are proved for the generalized fourier-bessel transform in the space (l^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

Abstract The integral transform method based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the generalized Weyl space-fractional operator. The solutions, representing ...

An approximation Ansatz for the operator solution, U(z′, z), of a hyperbolic first-order pseudodifferential equation, ∂z +a(z, x, Dx) with Re(a) ≥ 0, is constructed as the composition of global Fourier integral operators with complex phases. An estimate of the operator norm in L(H, H) of these operators is provided which allows to prove a convergence result for the Ansatz to U(z′, z) in some So...

The continuous spectrum, near its innmum, of the Lapla-cian for certain classes of`doubly-warped' complete Riemannian met-rics on the interiors of compact manifolds with boundary is examined using geometric optics. General conditions on the geometry of an algebra of vector elds leading to a calculus of pseudodiierential operators are described and, once veriied in this particular case, the asso...