integral(Omega) Mf (x)(p(x)) dx <= c(1) integral(Omega) vertical bar f (x)vertical bar(q(x)) dx + c(2),
A now classical result in the theory of variable Lebesgue spaces due to Lerner (2005) is that a modular inequality for the Hardy Littlewood maximal function in L-p(.) (R-n) holds if and only if the exponent is constant. We generalize this result and give a new and simpler proof. We then find necessary and sufficient conditions for the validity of the weaker modular inequality
Modular inequalities for the maximal operator in variable Lebesgue spaces
Fiorenza Alberto
2018
Abstract
A now classical result in the theory of variable Lebesgue spaces due to Lerner (2005) is that a modular inequality for the Hardy Littlewood maximal function in L-p(.) (R-n) holds if and only if the exponent is constant. We generalize this result and give a new and simpler proof. We then find necessary and sufficient conditions for the validity of the weaker modular inequalityFile in questo prodotto:
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