Mehriban N. Omarova

(L p , L q ) boundedness of the fractional maximal operator on the Laguerre hypergroup

Let 𝕂=[0, ∞)×ℝ be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group. In this paper we obtain necessary and sufficient conditions on the parameters for the boundedness of the fractional maximal operator on the Laguerre hypergroup from the spaces L p (𝕂) to the spaces L q (𝕂) and from the spaces L 1(𝕂) to the weak spaces WL q (𝕂).

Multilinear commutators of vector-valued intrinsic square functions on vector-valued generalized weighted Morrey spaces

In this paper, we will obtain the strong type and weak type estimates for vector-valued analogs of intrinsic square functions in the generalized weighted Morrey spaces Mwp,φ(l2). We study the boundedness of intrinsic square functions including the Lusin area integral, the Littlewood-Paley g-function and gλ∗ -function, and their multilinear commutators on vector-valued generalized weighted Morrey spaces Mwp,φ(l2). In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on φ(x,r) without assuming any monotonicity property of φ(x,r) on r.MSC:42B25, 42B35.

Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces

Abstract We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space W˙2,1p,φ(Q,ω)

Boundedness of vector-valued B-singular integral operators in Lebesgue spaces

\dot W_{2,1}^{p,\varphi }\left( {Q,\omega } \right)

Commutators and generalized local Morrey spaces

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On fractional maximal function and fractional integral on the Laguerre hypergroup

Abstract We study the vector-valued B-singular integral operators associated with the Laplace-Bessel differential operator △B=∑k=1n−1∂ 2∂x k 2+(∂2∂x n 2+2vxn∂∂x n),v>0.

Marcinkiewicz integrals associated with Schrödinger operator and their commutators on vanishing generalized Morrey spaces

\triangle_{B}=\sum\limits_{k=1}^{n-1}\frac{\partial^{2}}{\partial x_{k}^{2}}+(\frac{\partial^{2}}{\partial x_{n}^{2}}+\frac{2v}{x_{n}}\frac{\partial}{\partial x_{n}}) , v>0.

Gradient estimates for parabolic equations in generalized weighted Morrey spaces

We prove the boundedness of vector-valued B-singular integral operators A from Lp,v(R+n,H1)toLp,v(R+n,H2),