Jiecheng Chen

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We investigate the functions spaces on R for which the generalized partial derivatives Dk k f exist and belong to different Lorentz spacesΛkk w , where pk > 1 andw is nonincreasing and satisfies some special conditions. For the functions in these weighted Sobolev-Lorentz spaces, the estimates of the Besov type norms are found. The methods used in the paper(More)
As we know, this inequality is very important in Hp-theory, it is also a main difficulty in generalizing Hp-theory of one parameter to Hp -theory of several parameters, see [2, 6, 7, 8]. The first proof of (1) is probabilistic which was given by Burkholder, Gundy and Silverstein, see [1]; Fefferman and Stein first got an analytic proof of (1) by dealing(More)
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