| Autor: |
Mohammed Ali, Oqlah Al-Refai |
| Jazyk: |
angličtina |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Mathematics, Vol 7, Iss 10, p 886 (2019) |
| Druh dokumentu: |
article |
| ISSN: |
2227-7390 |
| DOI: |
10.3390/math7100886 |
| Popis: |
In this article, the boundedness of the generalized parametric Marcinkiewicz integral operators M Ω , ϕ , h , ρ ( r ) is considered. Under the condition that Ω is a function in L q ( S n - 1 ) with q ∈ ( 1 , 2 ] , appropriate estimates of the aforementioned operators from Triebel–Lizorkin spaces to L p spaces are obtained. By these estimates and an extrapolation argument, we establish the boundedness of such operators when the kernel function Ω belongs to the block space B q 0 , ν - 1 ( S n - 1 ) or in the space L ( l o g L ) ν ( S n - 1 ) . Our results represent improvements and extensions of some known results in generalized parametric Marcinkiewicz integrals. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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