Trace type Orlicz spaces and analysis of Orlicz spaces by Lebesgue exponents
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912464393732096 |
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| author | Petersson, Albin |
| author_facet | Petersson, Albin |
| contents | In the paper, we analyze the Lebesgue exponents $p_Φ$ and $q_Φ$, and show that for any $p_Φ< p < \infty$ and $1< q<q_Φ$, there exists an equivalent Young function $Ψ$ with $p < p_Ψ< \infty$ and $1<q_Ψ< q$. This type of construction is used to improve upon the inclusions $L^{p_Φ}\cap L^{q_Φ}\subseteq L^Φ\subseteq L^{p_Φ} + L^{q_Φ}$. For trace type Orlicz spaces $L^{Φ,Φ}$, we find that when $Φ\in Δ_2$, we have $L^{Φ,Φ} \subseteq L^Φ$ if and only if $Φ(||f||_{L^Φ}) \le C ρ_Φ(f)$ for all $f\in L^Φ$, and the reverse inclusion is equivalent to the reversed inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trace type Orlicz spaces and analysis of Orlicz spaces by Lebesgue exponents Petersson, Albin Functional Analysis In the paper, we analyze the Lebesgue exponents $p_Φ$ and $q_Φ$, and show that for any $p_Φ< p < \infty$ and $1< q<q_Φ$, there exists an equivalent Young function $Ψ$ with $p < p_Ψ< \infty$ and $1<q_Ψ< q$. This type of construction is used to improve upon the inclusions $L^{p_Φ}\cap L^{q_Φ}\subseteq L^Φ\subseteq L^{p_Φ} + L^{q_Φ}$. For trace type Orlicz spaces $L^{Φ,Φ}$, we find that when $Φ\in Δ_2$, we have $L^{Φ,Φ} \subseteq L^Φ$ if and only if $Φ(||f||_{L^Φ}) \le C ρ_Φ(f)$ for all $f\in L^Φ$, and the reverse inclusion is equivalent to the reversed inequality. |
| title | Trace type Orlicz spaces and analysis of Orlicz spaces by Lebesgue exponents |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2505.21764 |