Let G be a locally compact group, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\Phi _1, \Phi _2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi mathvariant="normal">Φ</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> be Young functions and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\nu , \omega $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ν</mi> <mo>,</mo> <mi>ω</mi> </mrow> </math></EquationSource> </InlineEquation> be moderate weight functions on G. In this paper, we investigate inclusion relations between the Orlicz amalgam spaces <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$W(L_{\nu }^{\Phi _1} (G), L_{\omega }^{\Phi _2} (G))$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mo stretchy="false">(</mo> <msubsup> <mi>L</mi> <mrow> <mi>ν</mi> </mrow> <msub> <mi mathvariant="normal">Φ</mi> <mn>1</mn> </msub> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <msubsup> <mi>L</mi> <mrow> <mi>ω</mi> </mrow> <msub> <mi mathvariant="normal">Φ</mi> <mn>2</mn> </msub> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with respect to Young functions, weights where the local and global components are the weighted Orlicz spaces <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$L_{\nu }^{\Phi _1}(G)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>L</mi> <mrow> <mi>ν</mi> </mrow> <msub> <mi mathvariant="normal">Φ</mi> <mn>1</mn> </msub> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$L_{\omega }^{\Phi _2}(G)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>L</mi> <mrow> <mi>ω</mi> </mrow> <msub> <mi mathvariant="normal">Φ</mi> <mn>2</mn> </msub> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, respectively. We also compare Orlicz amalgam spaces when G is a compact and discrete group. Our study generalizes and unifies the results that have been obtained for the Lebesgue spaces and the weighted Lebesgue spaces.

Inclusion Relations and Inequalities between Orlicz Amalgam Spaces

期刊论文
发表日期：

2025年12月7日

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Büşra Arıs,
Serap Öztop

摘要

Let G be a locally compact group, $\Phi _1, \Phi _2$ $Φ_{1}, Φ_{2}$ be Young functions and $\nu , \omega $ $ν, ω$ be moderate weight functions on G. In this paper, we investigate inclusion relations between the Orlicz amalgam spaces $W(L_{\nu }^{\Phi _1} (G), L_{\omega }^{\Phi _2} (G))$ $W (L_{ν}^{Φ_{1}} (G), L_{ω}^{Φ_{2}} (G))$ with respect to Young functions, weights where the local and global components are the weighted Orlicz spaces $L_{\nu }^{\Phi _1}(G)$ $L_{ν}^{Φ_{1}} (G)$ and $L_{\omega }^{\Phi _2}(G)$ $L_{ω}^{Φ_{2}} (G)$ , respectively. We also compare Orlicz amalgam spaces when G is a compact and discrete group. Our study generalizes and unifies the results that have been obtained for the Lebesgue spaces and the weighted Lebesgue spaces.