منابع مشابه
A ug 2 00 9 Adams inequalities on measure spaces
In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams’ results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels sati...
متن کامل2 9 Ju n 20 09 Adams inequalities on measure spaces
In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams’ results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels sati...
متن کاملSharp Singular Adams Inequalities in High Order Sobolev Spaces
In this paper, we prove a version of weighted inequalities of exponential type for fractional integrals with sharp constants in any domain of finite measure in R. Using this we prove a sharp singular Adams inequality in high order Sobolev spaces in bounded domain at critical case. Then we prove sharp singular Adams inequalities for high order derivatives on unbounded domains. Our results extend...
متن کاملHardy’s inequalities for monotone functions on partly ordered measure spaces
The theory of weighted inequalities for the Hardy operator, acting on monotone functions in R+, was first introduced in [2]. Extensions of these results to higher dimensions have been considered only in very specific cases: in particular, in the diagonal case, for p = 1 only (see [3]). The main difficulty in this context is that the level sets of the monotone functions are not totally ordered, ...
متن کاملHardy’s inequalities for monotone functions on partially ordered measure spaces
The theory of weighted inequalities for the Hardy operator, acting on monotone functions in R+, was first introduced in [2]. Extensions of these results to higher dimension have been considered only in very specific cases. In particular, in the diagonal case, only for p = 1 (see [5]). The main difficulty in this context is that the level sets of the monotone functions are not totally ordered, c...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2011
ISSN: 0001-8708
DOI: 10.1016/j.aim.2011.01.003