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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

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.

On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces

88%

Önal S., Vural Ç.

Open Mathematics

2013

tom 11

nr 9

1635-1642

We introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x ∈ X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of ω-rank, then X is metaLindelöf as well as a countable product of them. We also prove that if W satisfies ω-rank (F) and, for every x ∈ X, W(x) is of the form W 0(x) ∪ W 1(x), where W 0(x) is Noetherian and W 1(x) consists of neighbourhoods of x, then X is metacompact.

Ograniczanie wyników

2 Open Mathematics

1 Al-Dolat M.

1 Ali M.

1 Vural Ç.

1 Önal S.

1 2016

1 2013

Wyniki wyszukiwania

Parabolic Marcinkiewicz integrals on product spaces and extrapolation

On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces