Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces
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 ] , appropri...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-09-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/7/10/886 |
| _version_ | 1818334807447306240 |
|---|---|
| author | Mohammed Ali Oqlah Al-Refai |
| author_facet | Mohammed Ali Oqlah Al-Refai |
| author_sort | Mohammed Ali |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T14:13:24Z |
| format | Article |
| id | doaj.art-a538655c1d7d499e91f8aea71d7a5ce9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-13T14:13:24Z |
| publishDate | 2019-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a538655c1d7d499e91f8aea71d7a5ce92022-12-21T23:42:23ZengMDPI AGMathematics2227-73902019-09-0171088610.3390/math7100886math7100886Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to SurfacesMohammed Ali0Oqlah Al-Refai1Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, JordanDepartment of Mathematics, Faculty of Science, Taibah University, Almadinah Almunawwarah 41477, Saudi ArabiaIn 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.https://www.mdpi.com/2227-7390/7/10/886Lp boundednessrough kernelsMarcinkiewicz integralsTriebel–Lizorkin spacesextrapolation |
| spellingShingle | Mohammed Ali Oqlah Al-Refai Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces Mathematics Lp boundedness rough kernels Marcinkiewicz integrals Triebel–Lizorkin spaces extrapolation |
| title | Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces |
| title_full | Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces |
| title_fullStr | Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces |
| title_full_unstemmed | Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces |
| title_short | Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces |
| title_sort | boundedness of generalized parametric marcinkiewicz integrals associated to surfaces |
| topic | Lp boundedness rough kernels Marcinkiewicz integrals Triebel–Lizorkin spaces extrapolation |
| url | https://www.mdpi.com/2227-7390/7/10/886 |
| work_keys_str_mv | AT mohammedali boundednessofgeneralizedparametricmarcinkiewiczintegralsassociatedtosurfaces AT oqlahalrefai boundednessofgeneralizedparametricmarcinkiewiczintegralsassociatedtosurfaces |