Interpolation between <IMG BORDER="0" SRC="/proc/2004-132-10/S0002-9939-04-07425-8/gif-title0/img1.gif" > and <IMG BORDER="0" SRC="/proc/2004-132-10/S0002-9939-04-07425-8/gif-title0/img2.gif" >期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Interpolation between and

Authors:	Sergei V Astashkin Lech Maligranda

Institution:	Department of Mathematics, Samara State University, Akad. Pavlova 1, 443011 Samara, Russia ; Department of Mathematics, Lulela University of Technology, se-971 87 Lulea, Sweden

Abstract:	We show that if is a rearrangement invariant space on that is an interpolation space between $L_{1}$ and $L_{\infty}$ and for which we have only a one-sided estimate of the Boyd index $\alpha(X) > 1/p, 1 < p < \infty$ , then is an interpolation space between $L_{1}$ and $L_{p}$ . This gives a positive answer for a question posed by Semenov. We also present the one-sided interpolation theorem about operators of strong type and weak type $(p, p), 1 < p < \infty$ .

Keywords:	$L_{p}$-spaces Lorentz spaces rearrangement invariant spaces Boyd indices interpolation of operators operators of strong type operators of weak type $K$-functional Marcinkiewicz spaces

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