TAILIEUCHUNG - Weighted boundedness for a rough homogeneous singular integral

A weighted norm inequality for a homogeneous singular integral with a kernel belonging to a certain block space is proved. Also, some applications of this inequality are obtained. Our results are essential improvements as well as extensions of some known results on the weighted boundedness of singular integrals. | Turk J Math 29 (2005) , 75 – 97. ¨ ITAK ˙ c TUB Weighted Boundedness for a Rough Homogeneous Singular Integral Hussain Al-Qassem Abstract A weighted norm inequality for a homogeneous singular integral with a kernel belonging to a certain block space is proved. Also, some applications of this inequality are obtained. Our results are essential improvements as well as extensions of some known results on the weighted boundedness of singular integrals. Key Words: Singular integral, rough kernel, block space, weighted norm inequality. 1. Introduction Let Sn−1 denote the unit sphere in Rn (n ≥ 2) equipped with the normalized Lebesgue measure dσ = dσ(·). Throughout this paper, p0 will denote the dual exponent to p, that is 1/p + 1/p0 = 1. Also, we shall let Ω be a homogeneous function of zero which satisfies Ω ∈ L1 (Sn−1 ) and Z Ω (u) dσ (u) = 0. () Sn−1 For γ > 1, let ∆γ (R+ ) denote the set of all measurable functions h on R+ such that 1 sup R>0 R ZR γ

• Toán học
• Singular integral
• Rough kernel
• Block space
• Weighted norm inequality
• Homogeneous singular
• Riemann boundary
• Cauchy type integral
• Riemann problem
• Jordan curve
• Oscillatory integral
• Sub level set
• Explicit exponents
• Harmonis analysis
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