Modular Uniform Convexity of Lebesgue Spaces of Variable Integrability

Mostafa Bachar, Osvaldo Mendez, Messaoud Bounkhel
2018 Symmetry  
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.
doi:10.3390/sym10120708 fatcat:m66in2q5ung6jmnky23px5yst4