Modular Uniform Convexity of Lebesgue Spaces of Variable Integrability

We analyze the modular geometry of the Lebesgue space with variable exponent, L p ( · ) . Our central result is that L p ( · ) possesses a modular uniform convexity property. Part of the novelty is that the property holds even in the case sup x ∈ Ω p ( x ) = ∞ . We present specific applications to fixed point theory.

Modular Uniform Convexity of Lebesgue Spaces of Variable Integrability

We analyze the modular geometry of the variable exponent Lebesgue space Lp(.). We show that Lp(.) possesses a modular uniform convexity property. Part of the novelty is that the property holds even in the case supp(x) = ∞ . We present specific applications to fixed point theory. xÆΩ