This paper is concerned with the problem of finding a lower bound for certain matrix operators such as Hausdorff and Hilbert matrices on sequence spaces lp(w) and Lorentz sequence spaces d(w,p), which is recently considered in [7,8], similar to [13] considered by J. Pecaric, I. Peric and R. Roki. Also, this study is an extension of some works which are studied before in [1,2,7,8].

We study inhomogeneous Dirichlet boundary value problems associated to a linear parabolic equation dudt=Au with strongly elliptic operator A on bounded and unbounded domains white noise data. Our main assumption is that the heat kernel of corresponding homogeneous problem enjoys Gaussian type estimates taking into account distance boundary. Under mild assumptions about domain, we show generates...

The question of the basis property a system eigenfunctions one spectral problem for discontinuous second-order differential operator with parameter under discontinuity conditions is considered in weighted grand-Lebesgue spaces Lp),?(0, 1), 1 < p +?, general weight ?(?). These are non-separable and therefore it necessary to define its subspace associated equation. In this paper, using shift o...