Bellman function, Littlewood-Paley estimates and asymptotics for the Ahlfors-Beurling operator in L(C)
نویسندگان
چکیده
Estimation of L norms of Fourier multipliers is known to be hard. It is usually connected to some interesting types of PDE, see several such PDE for several Fourier multipliers on the line in a recent paper of Kalton and Verbitsky [13]. Sometimes, but much more rarely, one can establish sharp L estimates for Fourier multipliers in several variables. Riesz transforms are examples of success. They are defined in the following way. Choose k ∈ {1, ... , n}. The scalar Riesz transform Rk acts on a test function f (say, belonging to C∞ c or the Schwartz class S) by
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