The Bellman Functions and Two-weight Inequalities for Haar Multipliers
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چکیده
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 analysis, operator theory (including the perturbation of self-adjoint operators), and probability theory. The one-weight case is now pretty well understood for many interesting operators T0 . For the Hilbert transform Hf(t) = 1 π ∫
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Bellman Functions and Two Weight Inequalities for Haar Multipliers
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 ...
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