Let \(T_1, T_2\) be nonlinear integral operators of the form (2). There is estimated the expression \(\rho [\alpha(T_1 f - T_2 g)]\), where \(\rho\) is a modular on the space \(L^0(\Omega)\). This is applied in order to obtain a theorem concerning modular conservativity of a family \(T = (T_w)_{w\in W}\) of operators \(T\) w of the form (2).
In the present paper, we give criteria for the k−convexity of the Besicovitch-Orlicz space of almost periodic functions. Namely, it is shown that k-convexity is equivalent to strict convexity and reflexivity of this space in the case of Luxemburg norm.
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