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5 votes
1 answer
764 views

Looking for a reference for a version of the "The reverse Lebesgue dominated convergence theorem" for the Orlicz spaces

Please I need a reference where I can find a version of the "The reverse Lebesgue dominated convergence theorem" for the Orlicz spaces analogous to Theorem 1.2.7 in Semilinear Elliptic Equations for ...
Vrouvrou's user avatar
  • 277
2 votes
0 answers
183 views

Lyapounov's inequality for Orlicz norms

When a sequence $f \in \ell_1$, there is a very simple bound on its $\ell_q$-norms given by $\|f\|_q^q \leq \|f\|_1 \cdot \|f\|_\infty^{q-1}$. This inequality is a special (or rather limit) case of ...
ARG's user avatar
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3 votes
1 answer
162 views

Reference Request: $L^p(x)$/(Musielak–Orlicz space) analogue of classical $L^p$ result

Fix a non-empty open domain $\Omega\subseteq \mathbb{R}^d$ with compact closure, and a finite Borel measure $\mu$ on its closure $\overline{\Omega}$. In Halmos' book it is shown that: Classical ...
ABIM's user avatar
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