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MAXIMAL FUNCTIONS ALONG TWISTED SURFACES ON PRODUCT DOMAINS
Al-Salman, Ahmad Korean Mathematical Society 2021 대한수학회보 Vol.58 No.4
In this paper, we introduce a class of maximal functions along twisted surfaces in ℝ<sup>n</sup>×ℝ<sup>m</sup> of the form {(𝜙(|v|)u, 𝜑(|u|)v) : (u, v) ∈ ℝ<sup>n</sup>×ℝ<sup>m</sup>}. We prove L<sup>p</sup> bounds when the kernels lie in the space L<sup>q</sup> (𝕊<sup>n-1</sup>×𝕊<sup>m-1</sup>). As a consequence, we establish the L<sup>p</sup> boundedness for such class of operators provided that the kernels are in L log L(𝕊<sup>n-1</sup>×𝕊<sup>m-1</sup>) or in the Block spaces B<sup>0,0</sup><sub>q</sub> (𝕊<sup>n-1</sup>×𝕊<sup>m-1</sup>) (q > 1).
Singular and Marcinkiewicz integral operators on product domains
Badriya Al-Azri,Ahmad Al-Salman 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In this paper, we prove $L^{p}$ estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in $L(\log L)^{2}(\mathbb{S}^{n-1}\times \mathbb{S}^{m-1})$. Furthermore, we\ prove $L^{p}$ estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.
A Note on Marcinkiewicz Integral Operators on Product Domains
Badriya Al-Azri,Ahmad Al-Salman 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.4
In this paper we establish the Lp boundedness of Marcinkiewicz integral oper ators on product domains with rough kernels satisfying a weak size condition. We assume that our kernels are supported on surfaces generated by curves more general than polyno mials and convex functions. This generalizes and extends previous results.
Antioxidant and Hepatoprotective Effects of Murdannia bracteata Methanol Extract
Mun Fei Yam,Lee Fung Ang,Chung Pin Lim,Omar Ziad Ameer,Ibrahim Muhammad Salman,Mahfoudh Al-musli Mohammed,Mohd. Zaini Asmawi,Muthanna Fawzy Abdulkarim,Ghassan Zuhair Abdullah,Mariam Ahmad 사단법인약침학회 2010 Journal of Acupuncture & Meridian Studies Vol.3 No.3
Murdannia bracteata (C. B. Clarke) is a local plant that is widely used in Malaysia as a traditional remedy for various diseases of the kidney and liver, including inflammation and cancer. In the present study, we investigated the antioxidant and hepatoprotective activities of M. bracteata methanol extract (MB). 2,2’-diphenyl-1-picrylhydrazyl radical scavenging activity, lipid peroxidation inhibition and trolox equivalent antioxidant capacity of MB were determined. The hepatoprotective activity of MB was studied using a CCl4-induced liver toxicity model in rats. The hepatoprotective effect was assessed by monitoring the plasma malondialdehyde level and serum alanine transaminase and aspartate transaminase activities. Histopathological changes of hepatic tissue were also investigated. The results indicated that MB possessed potential antioxidant, lipid peroxidation inhibition and free radical scavenging activities. Pretreatment of rats with MB (500 mg/kg and 1000 mg/kg per os) before induction of CCl4-induced hepatotoxicity showed a dosedependent reduction in the necrotic changes in hepatic tissue. The increases in plasma malondialdehyde level, serum alanine transaminase and aspartate transaminase activities were also significantly inhibited by MB. The total phenolic content of MB determined using Folin-Ciocalteu assay was found to be 10%. The results of the present study indicated that the hepatoprotective effect of MB is most likely due to its antioxidant and free radical scavenging properties.