Weighted inequalities for some integral operators with rough kernels

María Riveros; Marta Urciuolo

Open Mathematics, Tome 12 (2014), p. 636-647 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper we study integral operators with kernels $K (x, y) = k_{1} (x - A_{1} y) \dots k_{m} (x - A_{m} y),$ $k_{i} (x) = {Ω_{i} (x) / |x|}^{n / q_{i}}$ where Ωi: ℝn → ℝ are homogeneous functions of degree zero, satisfying a size and a Dini condition, A i are certain invertible matrices, and n/q 1 +…+n/q m = n−α, 0 ≤ α < n. We obtain the appropriate weighted L p-L q estimate, the weighted BMO and weak type estimates for certain weights in A(p, q). We also give a Coifman type estimate for these operators.

Publié le : 2014-01-01

Zbl 1284.42040

EUDML-ID : urn:eudml:doc:269403

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     author = {Mar\'\i a Riveros and Marta Urciuolo},
     title = {Weighted inequalities for some integral operators with rough kernels},
     journal = {Open Mathematics},
     volume = {12},
     year = {2014},
     pages = {636-647},
     zbl = {1284.42040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0362-1}
}

María Riveros; Marta Urciuolo. Weighted inequalities for some integral operators with rough kernels. Open Mathematics, Tome 12 (2014) pp. 636-647. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0362-1/

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