## Linear Operators, Part 1 |

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Page 360

oO for each e > 0. |z—wl =e 22

AC. Show that there exists a finite constant K such that for f in CBV, |(S,f)(c) = K(v(f

, [0, *)+...op. f(a)), 0 < x < 2:t. 23

oO for each e > 0. |z—wl =e 22

**Suppose**that (S,f)(a) -> f(a) uniformly for every f inAC. Show that there exists a finite constant K such that for f in CBV, |(S,f)(c) = K(v(f

, [0, *)+...op. f(a)), 0 < x < 2:t. 23

**Suppose**that (i) (S,f)(a) -> f(a) uniformly in a for ...Page 598

operator. Let à e o (T), and lim, ... g.,(2) # 0. Show that A is a pole of q(T), and that

E(2; T)3 has a positive finite dimension. (Hint. See Exercise VII.5.35.) 3 Show that

if g ...

**Suppose**that g,(T) converges in the uniform operator topology to a compactoperator. Let à e o (T), and lim, ... g.,(2) # 0. Show that A is a pole of q(T), and that

E(2; T)3 has a positive finite dimension. (Hint. See Exercise VII.5.35.) 3 Show that

if g ...

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Then for f in L, we have lim to so... [...?(n-A),...,t(1,-i,0)f(u,...,y)\,...du, t—-co = f(r1, ...,

rn) for almost all ar. 7 (Hardy-Littlewood) Let h be a harmonic function defined in

the circle a "+y” < 1, and let 1 < p < 00.

Then for f in L, we have lim to so... [...?(n-A),...,t(1,-i,0)f(u,...,y)\,...du, t—-co = f(r1, ...,

rn) for almost all ar. 7 (Hardy-Littlewood) Let h be a harmonic function defined in

the circle a "+y” < 1, and let 1 < p < 00.

**Suppose**that s;"|h (re")|"d0 < K, 0 < r < 1.### What people are saying - Write a review

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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