On the maximal function for rotation invariant measures in $ℝ^{n}$

• Autorzy: Ana M. Vargas
• Języki publikacji: EN

Abstrakty

EN

Given a positive measure μ in $ℝ^n$, there is a natural variant of the noncentered Hardy-Littlewood maximal operator $M_{μ}f(x) = sup_{x ∈ B} 1/μ(B) ʃ_{B} |f|dμ$, where the supremum is taken over all balls containing the point x. In this paper we restrict our attention to rotation invariant, strictly positive measures μ in $ℝ^n$. We give some necessary and sufficient conditions for $M_μ$ to be bounded from $L^{1}(dμ)$ to $L^{1,∞}(dμ)$.

Słowa kluczowe

EN

maximal operators; weak type estimates

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 110
• Numer: 1
• Strony: 9-17

Daty

wydano

1994

otrzymano

1992-10-12

poprawiono

1993-12-12

Twórcy

autor

Ana M. Vargas

• Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Bibliografia

• [M-S] B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17-92.
• [S] P. Sjögren, A remark on the maximal function for measures in $ℝ^n$, Amer. J. Math. 105 (1983), 1231-1233.