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Parabolic Marcinkiewicz integrals on product spaces and extrapolation

100%
Ali M., Al-Dolat M.
Open Mathematics
|
2016
|
tom 14
|
nr 1
649-660
EN
In this paper, we study the the parabolic Marcinkiewicz integral [...] MΩ,hρ1,ρ2 ${\cal M}_{\Omega, h}^{{\rho _{1,}}{\rho _2}}$ on product domains Rn × Rm (n, m ≥ 2). Lp estimates of such operators are obtained under weak conditions on the kernels. These estimates allow us to use an extrapolation argument to obtain some new and improved results on parabolic Marcinkiewicz integral operators.
2
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General numerical radius inequalities for matrices of operators

81%
Al-Dolat M., Al-Zoubi K., Ali M., Bani-Ahmad F.
Open Mathematics
|
2016
|
tom 14
|
nr 1
109-117
EN
Let Ai ∈ B(H), (i = 1, 2, ..., n), and [...] T=[ 0 ⋯ 0 A 1 ⋮ ⋰ A 2 0 0 ⋰ ⋰ ⋮ A n 0 ⋯ 0 ] $ T = \left[ {\matrix{ 0 & \cdots & 0 & {A_1 } \cr \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {A_2 } & 0 \cr 0 & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots \cr {A_n } & 0 & \cdots & 0 \cr } } \right] $ . In this paper, we present some upper bounds and lower bounds for w(T). At the end of this paper we drive a new bound for the zeros of polynomials.
3
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On graded P-compactly packed modules

81%
Al-Zoubi K., Jaradat I., Al-Dolat M.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded P-compactly packed modules and we give a number of results concerning such graded modules. In fact, our objective is to investigate graded P-compactly packed modules and examine in particular when graded R-modules are P-compactly packed. Finally, we introduce the concept of graded finitely P-compactly packed modules and give a number of its properties.
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