On the membership of Hankel operators in a class of Lorentz ideals

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• 作者：Quanlei Fang^a ; ^{quanlei.fang@bcc.cuny.edu" class="auth_mail} ; Jingbo Xia^b ; ^{jxia@acsu.buffalo.edu" class="auth_mail}
• 关键词：Hankel operator ; Lorentz ideal
• 刊名：Journal of Functional Analysis
• 出版年：15 August 2014
• 年：2014
• 卷：267
• 期：4
• 页码：1137-1187
• 全文大小：707 K

文摘

Recall that the Lorentz ideal class="mathmlsrc">w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123614002092&_mathId=si1.gif&_user=111111111&_pii=S0022123614002092&_rdoc=1&_issn=00221236&md5=239a1ab9c3bb828e30129b636e340bdc">class="imgLazyJSB inlineImage" height="18" width="21" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022123614002092-si1.gif">cript>cal-align:bottom" width="21" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614002092-si1.gif">cript>class="mathContainer hidden">class="mathCode">croll">w>cript">Cw>w>pw>w>−w> is the collection of operators A   satisfying the condition class="mathmlsrc">w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123614002092&_mathId=si2.gif&_user=111111111&_pii=S0022123614002092&_rdoc=1&_issn=00221236&md5=24c52a24c41c75a3ebeb3905df650c16">class="imgLazyJSB inlineImage" height="23" width="246" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022123614002092-si2.gif">cript>cal-align:bottom" width="246" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614002092-si2.gif">cript>class="mathContainer hidden">class="mathCode">croll">w>chy="false">鈥?/mo>Achy="false">鈥?/mo>w>w>pw>w>−w>=w>∑w>w>j=1w>w>∞w>w>jw>w>−chy="false">(p−1chy="false">)chy="false">/pw>w>sw>w>jw>chy="false">(Achy="false">)<∞. Consider Hankel operators class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123614002092&_mathId=si3.gif&_user=111111111&_pii=S0022123614002092&_rdoc=1&_issn=00221236&md5=3c6cb185cf190bfc357b01609fff0f52" title="Click to view the MathML source">H_f:H²(S)→L²(S,d蟽)鈯朒²(S)class="mathContainer hidden">class="mathCode">croll">w>Hw>w>fw>:w>Hw>w>2w>chy="false">(Schy="false">)chy="false">→w>Lw>w>2w>chy="false">(S,d蟽chy="false">)鈯?/mo>w>Hw>w>2w>chy="false">(Schy="false">), where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123614002092&_mathId=si4.gif&_user=111111111&_pii=S0022123614002092&_rdoc=1&_issn=00221236&md5=fff49e0fc0960736ce6e49adfebf2f2d" title="Click to view the MathML source">H²(S)class="mathContainer hidden">class="mathCode">croll">w>Hw>w>2w>chy="false">(Schy="false">) is the Hardy space on the unit sphere S   in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123614002092&_mathId=si5.gif&_user=111111111&_pii=S0022123614002092&_rdoc=1&_issn=00221236&md5=b419ed4fb416f33d816b91502e760143" title="Click to view the MathML source">Cⁿclass="mathContainer hidden">class="mathCode">croll">w>Cw>w>nw>. In this paper we characterize the membership class="mathmlsrc">w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123614002092&_mathId=si6.gif&_user=111111111&_pii=S0022123614002092&_rdoc=1&_issn=00221236&md5=2bcea2248f36ec437f2e0487a8ab5a6b">class="imgLazyJSB inlineImage" height="18" width="62" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022123614002092-si6.gif">cript>cal-align:bottom" width="62" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614002092-si6.gif">cript>class="mathContainer hidden">class="mathCode">croll">w>Hw>w>fw>∈w>cript">Cw>w>pw>w>−w>, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123614002092&_mathId=si7.gif&_user=111111111&_pii=S0022123614002092&_rdoc=1&_issn=00221236&md5=8e3ac10979b769fa06c0fd37a76d0ebb" title="Click to view the MathML source">2n<p<∞class="mathContainer hidden">class="mathCode">croll">2n<p<∞.