Geodesic
On a Class of Singular Integral Operators With Rough Kernels
Canadian mathematical bulletin, Tome 49 (2006) no. 1, pp. 3-10

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In this paper, we study the ${{L}^{p}}$ mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces. We prove that our operators are bounded on ${{L}^{p}}$ provided that their kernels satisfy a size condition much weaker than that for the classical Calderón–Zygmund singular integral operators. Moreover, we present an example showing that our size condition is optimal. As a consequence of our results, we substantially improve a previously known result on certain maximal functions.
DOI : 10.4153/CMB-2006-001-9
Mots-clés : 42B20, 42B15, 42B25, Singular integrals, Rough kernels, Square functions, Maximal functions, Block spaces 
Al-Salman, Ahmad. On a Class of Singular Integral Operators With Rough Kernels. Canadian mathematical bulletin, Tome 49 (2006) no. 1, pp. 3-10. doi: 10.4153/CMB-2006-001-9
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