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Selected Papers of Antoni Zygmund by A. P. Calderón, A. Zygmund (auth.), A. Hulanicki, P.

By A. P. Calderón, A. Zygmund (auth.), A. Hulanicki, P. Wojtaszczyk, W. Żelazko (eds.)

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Zygmund. 98 and since [f (P)]y = y for y :::; f (P), and [f (P)]y = f (P) for y 2': f (P), the right hand side of the last expression can be replaced by J[f(P)P + 2 ~ pf(P)"] dP = Cl = C12 ~ pJ f(P)V dP. ~ ~ To estimate the second integral, we set y = {J, (x) and get 00 00 J{J'(y)pyv-1dy= - J xdfJJ(x). o Now 0 x X {Jf(x) = x ~-l [J t* (t) dtr:::; Jr (t)" dt, o and since f (p) belongs to L" so does we have r (t), 0 and x fJJ (x) -+ 0 as x -+ O. (x)dx o 0 and by a familiar theorem of Hardy (See [7], p.

It is enough to say, in connection with the questions which interest us, that for almost fifty years, up to 1915, the lectures at the university of \Varsaw were not given in Polish. While there were prominent Polish mathematicians in the first half of the nineteenth century (one may mention the name of \VRONSKI), the second half of it saw a change for the worse. Many scientists, among them mathematicians, in order to do their research, had to emigrate. Some of them kept contact with th~ old country and so preserved the scientific tradition there.

2) is replaced by the quadrant O

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