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Maximal Lp -regularity for parabolic equations, Fourier multiplier theorems and H ∞ -functional calculus. , 1855, Springer, Berlin, 2004. , Counterexamples concerning sectorial operators. Arch. Math. (Basel) 71 (1998), no. 5, 388–398. , Sur les multiplicateurs des séries de Fourier. Studia Math. 8 (1939), 78–91. [45] McConnell, T. , On Fourier multiplier transformations of Banachvalued functions. Trans. Amer. Math. Soc. 285 (1984), no. 2, 739–757. , Sharp estimates in vector Carleson imbedding theorem and for vector paraproducts.

Studia Math. 161 (2004), no. 1, 71– 97. , Marcinkiewicz and Mihlin multiplier theorems, and Rboundedness. Evolution equations: applications to physics, industry, life sciences and economics (Levico Terme, 2000), 403–413, Progr. , 55, Birkhäuser, Basel, 2003. , Operator-valued Fourier multiplier theorems and maximal Lp regularity. Math. Ann. 319 (2001), no. 4, 735–758. , The H ∞ holomorphic functional calculus for sectorial operators – a survey. Partial Differential Equations and Functional Analysis, The Philippe Clément Festschrift, 263–294, Oper.

In the case that we don’t take the complex conjugate of the complex coefficients of the standard basis, we use the symbol uC = S uS eS for u = S uS eS with uS ∈ C. Then for the vector u = nj=0 uj ej we have n uuC = u2j . j=0 If uuC is not a negative real number or zero, then the square root of the complex number uuC with positive real part is denoted by |u|C and |u|C = 0 if uuC = 0. The Clifford algebra C (Cn ) is a complex vector space with a basis eS , S ⊂ {1, . . , n} given by eS = ej1 · · · ejk if S = {j1 , .

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