Weighted inequalities for some integral operators with rough kernels

• Autorzy: María Riveros , Marta Urciuolo
• Języki publikacji: EN

Abstrakty

EN

In this paper we study integral operators with kernels $$K(x,y) = k_1 (x - A_1 y) \cdots k_m \left( {x - A_m y} \right),$$ $$k_i \left( x \right) = {{\Omega _i \left( x \right)} \mathord{\left/ {\vphantom {{\Omega _i \left( x \right)} {\left| x \right|}}} \right. \kern-\nulldelimiterspace} {\left| x \right|}}^{{n \mathord{\left/ {\vphantom {n {q_i }}} \right. \kern-\nulldelimiterspace} {q_i }}}$$ 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.

Słowa kluczowe

EN

Fractional operators; Calderón-Zygmund operators; BMO; Muckenhoupt weights

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 4
• Strony: 636-647

Daty

wydano

2014-04-01

online

2014-01-17

Twórcy

autor

María Riveros

• Universidad Nacional de Córdoba, CIEM (CONICET), Medina Allende y Haya de la Torre

autor

Marta Urciuolo

• Universidad Nacional de Córdoba, CIEM (CONICET), Medina Allende y Haya de la Torre

Bibliografia

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• [10] Riveros M.S., Urciuolo M., Weighted inequalities for integral operators with some homogeneous kernels, Czechoslovak Math. J., 2005, 55(130)(2), 423–432 http://dx.doi.org/10.1007/s10587-005-0032-y
• [11] Riveros M.S., Urciuolo M., Weighted inequalities for fractional type operators with some homogeneous kernels, Acta Math. Sin. (Engl. Ser.), 2013, 29(3), 449–460 http://dx.doi.org/10.1007/s10114-013-1639-9
• [12] Rocha P., Urciuolo M., On the H p-L q boundedness of some fractional integral operators, Czechoslovak Math. J., 2012, 62(137)(3), 625–635 http://dx.doi.org/10.1007/s10587-012-0054-1
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Identyfikatory

DOI

10.2478/s11533-013-0362-1