double system of exponents with complex-valued coefficients is considered. under some conditions on the coefficients, we prove that if this system forms a basis for the morrey-lebesgue type space on $left[-pi , pi right]$, then it is isomorphic to the classical system of exponents in this space.

Double system of exponents with complex-valued coefficients is considered. Under some conditions on the coefficients, we prove that if this system forms a basis for the Morrey-Lebesgue type space on $left[-pi , pi right]$, then it is isomorphic to the classical system of exponents in this space.

We find conditions for the embedding of grand Morrey-type spaces into so-called local Lebesgue spaces.

Abstract Uniqueness of Leray solutions the 3D Navier-Stokes equations is a challenging open problem. In this article we will study problem for stationary in whole space R 3 . Under some additional hypotheses, stated terms Lebesgue and Morrey spaces, show that trivial solution U ? = 0 unique solution. This type results are known as Liouville theorems.

Abstract In this paper, the boundedness of Hausdorff operator on weak central Morrey space is obtained. Furthermore, we investigate bounds p -adic fractional weighted Lebesgue spaces. We also obtain sufficient condition commutators by taking symbol function from Lipschitz Moreover, strong type estimates for and its commutator Lorentz spaces are acquired.

In this paper, the boundedness properties of vector-valued intrinsic square functions and their commutators with \(BMO(\mathbb {R}^{n})\) are discussed. We first show weighted strong-type weak-type estimates in Morrey-type spaces. Then, we obtain analogues endpoint case, establish weak \(L\log L\)-type for these setting Lebesgue Furthermore, prove commutator operators particular, can Morrey spa...

In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators [Formula: see text] in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutator...

In this paper we give new characterization of the classical Morrey space. Complementary global Morrey-type spaces are introduced. It is proved that for particular values of parameters these spaces give new pre-dual space of the classical Morrey space. We also show that our new pre-dual space of the Morrey space coincides with known pre-dual spaces.

We establish some sharp maximal function inequalities for the Toeplitz type operator, which is related to certain fractional singular integral operator with general kernel. These results are helpful to investigate the boundedness of the operator on Lebesgue, Morrey and Triebel–Lizorkin spaces respectively.

We define a Muckenhoup-type condition on weighted Morrey spaces using the Köthe dual of space. show that is necessary and sufficient for boundedness maximal operator defined with balls centered at origin spaces. A modified characterizes inequalities Calderón operator. also local usual Hardy–Littlewood operator, simplifying previous characterization Nakamura–Sawano–Tanaka. For same in case globa...