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<p>We define the iterated (quasi)normed function spaces of<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1513_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">$ L_{p(\cdot)} $</EquationSource> </InlineEquation> <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1513_Article_IEq4.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="79" /> </InlineMediaObject> <EquationSource Format="TEX">$ (L_{q(\cdot)}(\dots)) $</EquationSource> </InlineEquation>-type with exponents depending on all variables.Also, we prove an&#xa0;analog of the Minkowski inequality for mixed norms and a&#xa0;multiplicative interpolation type inequalityin these spaces and use the relevant theorems for proving an embedding theoremfor the function spaces with variable smoothness depending on different directions.</p>

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Function Spaces of \( L_{p(\cdot)} \) \( (L_{q(\cdot)}) \)-Type and Embedding Theorems for Spaces with Variable Smoothness

  • 期刊论文

  • 发表日期：

    2025年1月29日

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  • A. N. Artyushin

摘要

We define the iterated (quasi)normed function spaces of $ L_{p(\cdot)} $ $ (L_{q(\cdot)}(\dots)) $ -type with exponents depending on all variables.Also, we prove an analog of the Minkowski inequality for mixed norms and a multiplicative interpolation type inequalityin these spaces and use the relevant theorems for proving an embedding theoremfor the function spaces with variable smoothness depending on different directions.