Abstract
In this paper, the sharp inequalities for some vector-valued multilinear integral operators are obtained. As applications, we get the weighted ( ) norm inequalities and an -type estimate for the vector-valued multilinear operators. MSC:42B20, 42B25.
Highlights
In this paper, the sharp inequalities for some vector-valued multilinear integral operators are obtained
We study some vector-valued multilinear integral operators as follows
For < s < ∞, the vector-valued multilinear operator related to Ft is defined by TA(f )(x) s =
Summary
For < s < ∞, the vector-valued multilinear operator related to Ft is defined by TA(f )(x) s =. The main purpose of this paper is to prove a sharp inequality for the vector-valued multilinear integral operators. We obtain the weighted Lp (p > ) norm inequalities and an L log L-type estimate for the vector-valued multilinear operators. The Young functions to be used in this paper are (t) = exp(tr) – and (t) = t logr(t + e), the corresponding -average and maximal functions are denoted by · exp Lr,Q, Mexp Lr and · L(log L)r,Q, ML(log L)r. For r ≥ , we denote that b oscexp Lr = sup b – bQ exp Lr,Q, the space Oscexp Lr is defined by Oscexp Lr = b ∈ L log Rn : b oscexp Lr < ∞.
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