Multidimensional Lusin-type inequalities for Grand Lebesgue Spaces

2015/02/10 by E. Ostrovsky, Ostrovsky, E., L Sirota +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1502.03145

arxiv created 2015/02/10 · arxiv updated 2015/02/12

Abstract

We generalize in this short paper the classical Luzin's theorem about existence of integral on the measurable function and its multidimensional analogues on the many popular classes of rearrangement invariant (r.i.) spaces, namely, on the so-called Grand Lebesgue Spaces.

Related

• Sharp Lyapunov's inequality for the measurable sets with infinite measure, with generalization to the Grand Lebesgue spaces
• Cpmposed Grand Lebesgue Spaces
• Generalized Grand Lebesgue Spaces norm estimations for some operators
• Effectivizing Lusin's Theorem
• Wirtinger-type inequalities for some rearrangement invariant spaces