Bruna , Korenblum : A note on Calderón-Zygmund singular integral convolution operatorsAbstract: The principal problem considered is the determination of all nonnegative functions, , such that where the functions are defined on , C is a constant independent of f and. The main result is that is such a function if and only if. References [Enhancements On Off] What's this? Coifman and C. Fefferman , Weighted norm inequalities for maximal functions and singular integrals , Studia Math. Fefferman and E.
On Weighted Convergence of Double Singular Integral Operators Involving Summation
In mathematics , singular integrals are central to harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular integral is an integral operator. Usually further assumptions are required to obtain results such as their boundedness on L p R n. The archetypal singular integral operator is the Hilbert transform H. More precisely,. The size condition on the Fourier transform of K. Property 1.
This chapter consists of five sections. First section is devoted to introduction part in which the description of the problem is presented and theoretical background is given. In the second section, the preliminary concepts which are utilized in the sequel are introduced. Then, the conditions under which double singular integral operators involving summation are well-defined in the space of Lebesgue measurable functions defined on different sets are presented. In the third section, Fatou type convergences of handled operators are discussed.
Singular Integrals, pg. The Littlewood-Paley Theory and Multipliers, pg. Differentiability Properties in Terms of Function Spaces, pg. Extensions and Restrictions, pg. Return to the Theory of Harmonic Functions, pg. Differentiation of Functions, pg.
Singular integrals are among the most interesting and important objects of study in analysis, one of the three main branches of mathematics. They deal with real.
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