# Questions tagged [orlicz-spaces]

For questions about Orlicz spaces, which are a generalization of classical Lebesgue spaces $\mathbb L^p$.

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### Definition and norm of an Orlicz space

Let me define the notions first, (1)$\textbf{Young Function:}$ A convex function $\Phi:\mathbb{R}\to \mathbb{R^+}$ is said to be a Young function if the following conditions satisfy : (a) $\Phi(0)=0$ (...
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### Example of a Young function which does not satisfy $\Delta_{2}$ condition

Let me define first (1) A convex function $\Phi \colon \mathbb{R}\to \mathbb{R}^+$ which satisfies the conditions, (a) $\Phi(0)=0$ (b)$\Phi(-x)=\Phi(x)$ (c) $\lim_{x \to \infty}\Phi(x)=+\infty$, is ...
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### Condition on the Young's function

I am reading the paper "Fractional integration in Orlicz spaces" by R. Sharpley. And I would like to understand one question: Let $A,B, C$ are Young's functions. The spaces $L_A, L_B$ are ...
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### In question (ii) why we need the condition that $\Phi$ to be delta 2 function to prove that space is vector space.

Question Image Can we prove it without that condition where is the problem?
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### Example of a Young's function under Lorentz-Shimogaki condition

I am reading about convolution operators and Orlicz spaces. And I would like to contract some example and stuck at some point. Let $\Psi(t)=\int_0^t\psi(s)$ be a Young's function. Then, $\Psi$ ...
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### Orlicz space property for locally compact discrete group $G$

A function $\varphi:\mathbb{R}\to[0,\infty]$ is called a Young function if $\varphi$ is convex, even,and left continuous with $\varphi(0)=0$, also let $G$ denote a locally compact group with a left ...
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### Analogue of Lebesgue differentiation theorem in Orlicz spaces

It is well known that $$\lim\limits_{r\rightarrow 0}\dfrac{\|f\chi_{B(x,r)}\|_{L_{p}(\mathbb{R}^{n})}}{\|\chi_{B(x,r)}\|_{L_{p}(\mathbb{R}^{n})}}=|f(x)|$$ for almost all $x\in\mathbb{R}^{n}$. Here \$\...
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