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Our aim is to study the modular inequalities for some operators, for examplethe Bergman projection acting on, in Lebesgue spaces with variable exponent.Under proper assumptions on the variable exponent, we prove that the modularinequalities are hold if and only if the exponent almost everywhere equals to aconstant. In order to get the main results, we prove a lemma for a lowerpointwise bound for these operators of a characteristic function.

Some mudular inequalities in Lebesgue spaces with variable exponent