A weighted bilinear gradient inequality. Issue 4 (24th July 2014)

• Record Type: Journal Article
• Authors: Salvador, Pedro Ortega
• Is Part Of: Proceedings. Volume 144:Issue 4(2014)
• Page Start: 819
• Page End: 829
• Publication Date: 2014-07-24
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210512001965
• Languages: English
• ISSNs: 0308-2105

Abstract

<abstract abstract-type="normal"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>We characterize the weights <italic>w</italic>₀, <italic>w</italic>₁, <italic>w</italic>₂ such that the weighted bilinear gradient inequality</p> <p> <disp-formula> <graphic mimetype="image" position="anchor" xlink:href="ark:/27927/pghw30g2ng" xlink:type="simple" orientation="portrait" xmlns:xlink="http://www.w3.org/1999/xlink" /> </disp-formula> </p> <p> <disp-formula> <graphic mimetype="image" position="anchor" xlink:href="ark:/27927/pghw30g2gw" xlink:type="simple" orientation="portrait" xmlns:xlink="http://www.w3.org/1999/xlink" /> </disp-formula> </p> <p>holds for all functions <inline-graphic xlink:href="ark:/27927/pghw30g2kf" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />, with a positive constant <italic>K</italic> independent of <italic>f</italic>₁ and <italic>f</italic>₂, for all possible values of <italic>q, p</italic>₁ and <italic>p</italic>₂ with 1 &lt; <italic>q, p</italic>₁, <italic>p</italic>₂ &lt; ∞.</p> </abstract>