Bellman Functions and Two Weight Inequalities for Haar Multipliers
نویسنده
چکیده
Weighted norm inequalities for singular integral operators appear naturally in many areas of analysis, probability, operator theory ect. The one-weight case is now pretty well understood, and the answers are given by the famous Helson–Szegö theorem and the Hunt–Muckenhoupt–Wheden Theorem. The fist one state that the Hilbert Transform H is bounded in the weighted space L(w) if and only if w can be represented as w = exp{u + Hv}, where u, v ∈ L, ‖u‖∞ < π/2. The Hunt–Muckenhoupt–Wheden Theorem states that the Hilbert transform H is bounded in L(w) if and only if the weight w satisfies the so-called Muckenhoupt Ap condition
منابع مشابه
The Bellman Functions and Two-weight Inequalities for Haar Multipliers
hold with some constant C independent of f? (Unless otherwise specified, all integrals are taken with respect to the standard Lebesgue measure on R.) Denoting w := u−1, we can reformulate the above question as follows: When is the operator T := M√vT0M√w bounded in L ? (Here Mφ stands for the operator of multiplication by φ.) Such weighted norm inequalities arise naturally in many areas of analy...
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