{"title":"变指数加权Morrey空间中的三角多项式逼近","authors":"Z. Çakir, C. Aykol, V. Guliyev, A. Serbetci","doi":"10.15330/cmp.13.3.750-763","DOIUrl":null,"url":null,"abstract":"In this paper we investigate the best approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces ${\\mathcal{M}}_{p(\\cdot),\\lambda(\\cdot)}(I_{0},w)$, where $w$ is a weight function in the Muckenhoupt $A_{p(\\cdot)}(I_{0})$ class. We get a characterization of $K$-functionals in terms of the modulus of smoothness in the spaces ${\\mathcal{M}}_{p(\\cdot),\\lambda(\\cdot)}(I_{0},w)$. Finally, we prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces ${\\mathcal{\\widetilde{M}}}_{p(\\cdot),\\lambda(\\cdot)}(I_{0},w),$ the closure of the set of all trigonometric polynomials in ${\\mathcal{M}}_{p(\\cdot),\\lambda(\\cdot)}(I_{0},w)$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"5 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces\",\"authors\":\"Z. Çakir, C. Aykol, V. Guliyev, A. Serbetci\",\"doi\":\"10.15330/cmp.13.3.750-763\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we investigate the best approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces ${\\\\mathcal{M}}_{p(\\\\cdot),\\\\lambda(\\\\cdot)}(I_{0},w)$, where $w$ is a weight function in the Muckenhoupt $A_{p(\\\\cdot)}(I_{0})$ class. We get a characterization of $K$-functionals in terms of the modulus of smoothness in the spaces ${\\\\mathcal{M}}_{p(\\\\cdot),\\\\lambda(\\\\cdot)}(I_{0},w)$. Finally, we prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces ${\\\\mathcal{\\\\widetilde{M}}}_{p(\\\\cdot),\\\\lambda(\\\\cdot)}(I_{0},w),$ the closure of the set of all trigonometric polynomials in ${\\\\mathcal{M}}_{p(\\\\cdot),\\\\lambda(\\\\cdot)}(I_{0},w)$.\",\"PeriodicalId\":42912,\"journal\":{\"name\":\"Carpathian Mathematical Publications\",\"volume\":\"5 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2021-12-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Carpathian Mathematical Publications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15330/cmp.13.3.750-763\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Carpathian Mathematical Publications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15330/cmp.13.3.750-763","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces
In this paper we investigate the best approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$, where $w$ is a weight function in the Muckenhoupt $A_{p(\cdot)}(I_{0})$ class. We get a characterization of $K$-functionals in terms of the modulus of smoothness in the spaces ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$. Finally, we prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces ${\mathcal{\widetilde{M}}}_{p(\cdot),\lambda(\cdot)}(I_{0},w),$ the closure of the set of all trigonometric polynomials in ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$.