Some weighted norm inequalities for a one-sided version of $g*_{λ}$

• Autorzy: L. de Rosa , C. Segovia
• Języki publikacji: EN

Abstrakty

EN

We study the boundedness of the one-sided operator $g⁺_{λ,φ}$ between the weighted spaces $L^{p}(M¯w)$ and $L^{p}(w)$ for every weight w. If λ = 2/p whenever 1 < p < 2, and in the case p = 1 for λ > 2, we prove the weak type of $g⁺_{λ,φ}$. For every λ > 1 and p = 2, or λ > 2/p and 1 < p < 2, the boundedness of this operator is obtained. For p > 2 and λ > 1, we obtain the boundedness of $g⁺_{λ,φ}$ from $L^{p}((M¯)^{[p/2]+1} w)$ to $L^{p}(w)$, where $(M¯)^{k}$ denotes the operator M¯ iterated k times.

Kategorie tematyczne

• 26A33: Fractional derivatives and integrals
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 176
• Numer: 1
• Strony: 21-36

Daty

wydano

2006

Twórcy

autor

L. de Rosa

• Juan José Olleros 2969 8 B, 1426 Buenos Aires, Argentina

autor

C. Segovia

• Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
• Instituto Argentino de Matemática, CONICET, Saavedra 15 3er Piso, 1083 Buenos Aires, Argentina

Identyfikatory

DOI

10.4064/sm176-1-2