Equivalent norms in polynomial spaces and applications

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• 作者：Gustavo Ara&uacute ; jo^a ; ¹ ; ^{gdasaraujo@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; P. Jimé ; nez-Rodrí ; guez^b ; ^{pjimene1@kent.edu" class="auth_mail" title="E-mail the corresponding author} ; Gustavo A. Muñ ; oz-Ferná ; ndez^c ; ² ; ^{gustavo_fernandez@mat.ucm.es" class="auth_mail" title="E-mail the corresponding author} ; Juan B. Seoane-Sep&uacute ; lveda^d ; ^c ; ² ; ^{jseoane@mat.ucm.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Norms ; Absolutely summing operators ; Bohnenblust&ndash ; Hille inequality ; Hardy&ndash ; Littlewood inequality
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：445
• 期：2
• 页码：1200-1220
• 全文大小：519 K

文摘

In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy–Littlewood constants for 2-homogeneous polynomials on b=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16002687&_mathId=si1.gif&_user=111111111&_pii=S0022247X16002687&_rdoc=1&_issn=0022247X&md5=7277583c2040239b0f041ee0b147fdbc"> spaces, b=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16002687&_mathId=si2.gif&_user=111111111&_pii=S0022247X16002687&_rdoc=1&_issn=0022247X&md5=695d2e564c2f09ac586f247a9fc6eeda" title="Click to view the MathML source">2<p≤∞$2<p\le \infty$. We also provide lower estimates for the Hardy–Littlewood constants for polynomials of higher degrees.