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A.P. Calderon adjoint antisymmetric belongs to BMO BMO function boundary value problem bounded factor bounded function bounded operator bounded subset Calderon-Zygmund operator Carleson measure Cauchy integral Cauchy-Schwarz inequality Ching proved class of operators clear Coifman coincides completes the proof condition 2.17 continuity properties cube Definition degree zero denotes diagonal difficult to show distribution kernel dydx estimate in 4.5 exists fact Fourier transform function q(x functional spaces given f e given f,g e Hilbert transform homogeneous function hypothesis kernel k(x,y,t lacunary series Laplace operator Let us consider Let us fix Let us prove Lf(x linear and continuous linear continuous operator linear partial differential Meyer Moreover mth commutator notion of Calderon-Zygmund obtain operator associated original proof PERNAMBUCO Poisson kernel positive measures Proof of Theorem pseudo-differential operator radial function reasonable function f space suffices to prove supp supp(f suppose Theorem 4.1 THEOREM Josefina VVBP weak sense