Algebraic genericity of strict-order integrability

• Autorzy: Luis Bernal-González
• Języki publikacji: EN

Abstrakty

EN

We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space $L^{p}(μ,X)$ (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of $L^{p}(μ,X)$ (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological space and μ is a Borel measure on X with appropriate properties.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)
• 28A25: Integration with respect to measures and other set functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 199
• Numer: 3
• Strony: 279-293

Daty

wydano

2010

Twórcy

autor

Luis Bernal-González

• Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain

Identyfikatory

DOI

10.4064/sm199-3-5