Large structures made of nowhere $L^{q}$ functions

• Autorzy: Szymon Głąb , Pedro L. Kaufmann , Leonardo Pellegrini
• Języki publikacji: EN

Abstrakty

EN

We say that a real-valued function f defined on a positive Borel measure space (X,μ) is nowhere q-integrable if, for each nonvoid open subset U of X, the restriction $f|_U$ is not in $L^{q}(U)$. When (X,μ) has some natural properties, we show that certain sets of functions defined in X which are p-integrable for some p's but nowhere q-integrable for some other q's (0 < p,q < ∞) admit a variety of large linear and algebraic structures within them. The presented results answer a question of Bernal-González, improve and complement recent spaceability and algebrability results of several authors and motivate new research directions in the field of spaceability.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 15A03: Vector spaces, linear dependence, rank

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 221
• Numer: 1
• Strony: 13-34

Daty

wydano

2014

Twórcy

autor

Szymon Głąb

• Institute of Mathematics, Technical University of Łódź, Wólczańska 215, 93-005 Łódź, Poland

autor

Pedro L. Kaufmann

• CAPES Foundation, Ministry of Education of Brazil, Brasília/DF 70040-020, Brazil
• Institute de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France

autor

Leonardo Pellegrini

• Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-900, São Paulo, Brazil

Identyfikatory

DOI

10.4064/sm221-1-2