we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

In this paper, we study spectral decompositions with respect to a system of generalized eigenvectors second-order differential operators on an interval whose resolvents possess convolution representations. We obtain the representation integral boundary conditions. Then, using generated by initial operator, construct Fourier transform. A connection between operation in original functional space ...

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

In this paper we deal with a definition of Lp-Fourier transform on locally compact groups. Recall that, for locally compact abelian groups, the Hausdorff-Young inequality reads: Let 1 < p < 2 and q = p/(p − 1). If g ∈ L1(G) ∩ Lp(G), then ĝ ∈ Lq(Ĝ), with ‖ĝ‖q ≤ ‖g‖p. The inequality allows to extend the Fourier transform to a continuous operator Fp : Lp → Lq by continuity. It was generalized to t...

A numerical framework for studying plasma flows in electric propulsion systems is developed. The novelty of this kinetic-theory-based method is the spectral treatment of the Boltzmann collision operator using Fourier-Galerkin scheme coupled with the computational efficiency of the streaming of the lattice Boltzmann method. This spectral treatment (i) avoids the low Mach number restriction of th...