On geometric properties of the spaces L p(x)

Abstract

We study the reflexivity, the uniform convexity, the Daugavet property and the Radon-Nikodym property of the generalized Lebesgue spaces L p(x) .

Modular Uniform Convexity of Lebesgue Spaces of Variable Integrability

“…For the variable exponent spaces L p(•) (Ω), uniform convexity is fully characterized. The reader is referred to [14,19] for the proof of the next Theorem. Notice that it follows that the uniform convexity of the Luxemburg normnin expression (5) is equivalent to the ∆ 2 -condition.…”

Modular Uniform Convexity of Lebesgue Spaces of Variable Integrability

“…The number δ X (ε) is known as the modulus of uniform convexity of X (see, for example, [4] and [7]). For the variable exponent spaces L p(•) (Ω), uniform convexity is fully characterized: We refer the reader to [10] for the proof of the following theorem, from which it follows that the uniform convexity of the Luxemburg norm (5) is equivalent to the ∆ 2 -condition.…”

On Well Posed Impulsive Boundary Value Problems for P(t)-Laplacian's

“…For some background material concerning Orlicz-Sobolev spaces we refer to [8] and [12,15]. Let a ∈ L ∞ + (0, π).…”