Modular inequalities for the maximal operator in variable Lebesgue spaces
作者： David Cruz-Uribe , Giovanni Di Fratta , Alberto Fiorenza
关键词: Maximal operator 、 Variable (mathematics) 、 Lp space 、 Combinatorics 、 Mathematics 、 Constant (mathematics) 、 Maximal function 、 Bounded function 、 Exponent 、 Operator (physics)
摘要: Abstract A now classical result in the theory of variable Lebesgue spaces due to Lerner (2005) is that a modular inequality for Hardy–Littlewood maximal function L p ( ⋅ ) R n holds if and only exponent constant. We generalize this give new simpler proof. then find necessary sufficient conditions validity weaker ∫ Ω M f x d ⩽ c 1 | q + 2 , where are non-negative constants any subset . As corollary we get T operator bounded on ∞
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