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math.CA2012
Endpoint bounds for the quartile operator
Ciprian Demeter, Francesco Di Plinio
It is a result by Lacey and Thiele that the bilinear Hilbert transform maps L^{p_1}(R) \times L^{p_2}(R) into L^{p_3}(R) whenever (p_1,p_2,p_3) is a Holder tuple with p_1,p_2 > 1 a…
math.CA2012
Logarithmic L^p bounds for maximal directional singular integrals in the plane
Ciprian Demeter, Francesco Di Plinio
We discuss the L^p-boundedness of maximal singular integrals in the plane over a finite set V of N directions. Logarithmic bounds are established for a set V of arbitrary structure…