Read e-book online The Carleson-Hunt Theorem on Fourier Series PDF

By Ole Groth Jørsboe

ISBN-10: 0387111980

ISBN-13: 9780387111988

ISBN-10: 3540111980

ISBN-13: 9783540111986

Show description

Read or Download The Carleson-Hunt Theorem on Fourier Series PDF

Best mathematics books

W. W. Rouse Ball's Recreations mathematiques et problemes des temps anciens et PDF

Nous publions une nouvelle édition de l. a. traduction française de l'ouvrage si remarquable de Rouse-Ball, faite sur l. a. 4e édition anglaise. M. Filz Patrick ne s'est pas borné au rôle de traducteur, il a enrichi F ouvrage d'additions nombreuses et importantes. Dans cette première partie, notamment, il a introduit une histoire originale cl anecdotique des nombres, et plus de cent problèmes extrêmement curieux, dont l. a. resolution, bien qu'élémentaire, est parfois délicate.

Mathematical and computational techniques for multilevel by Ullrich Rüde PDF

Multilevel adaptive equipment play an more and more very important function within the resolution of many medical and engineering difficulties. quick adaptive equipment ideas are ordinary by means of experts to execute and learn simulation and optimization difficulties. This monograph provides a unified method of adaptive equipment, addressing their mathematical concept, effective algorithms, and versatile facts constructions.

Tsuneyoshi Nakayama, Hiroyuki Shima (auth.)'s Higher Mathematics for Physics and Engineering: Mathematical PDF

End result of the quick growth of the frontiers of physics and engineering, the call for for higher-level arithmetic is expanding every year. This publication is designed to supply available wisdom of higher-level arithmetic demanded in modern physics and engineering. Rigorous mathematical buildings of significant topics in those fields are absolutely lined, with a view to be valuable for readers to develop into accustomed to sure summary mathematical strategies.

Extra info for The Carleson-Hunt Theorem on Fourier Series

Example text

Furthermore. 17). 2 that llHyf-Qy fll~ ~ l[0fll~ ~ 321]fI]~ < +~ . and thus llHyf -Qy f]I2 § 0 as y ~0+ by dominated convergence. 14). P2yf dx . 15). 16). 4. 16). 13) proved . 39 Proof. 13). is of weak type is of type 1 . 15) in 2 , and hence also of weak type 2 . e. Hf dx[ = < cp llfllp llgllq we conclude fs and all and g~Lq(R) H . Hgdx[ = llfIlp<__l proving that (I

Is continuous. 20) is unaffected, if we from any continuous function fo f subtract of compact support. , proving the lena. 4. e. the operator Proof. P for all P Y is of strong type p Using H~ider's inequality we get for for all p ~ ]I,+ ~] p ~ ]I,+~[ IPyf(x)]P< ([ +~k (x-t). 5. 2. In fact, llPyfllp ~ II0 flip ~ Cpllfllp , p E ]I,+~] However~ we do not get that the constant may be chosen equal I . 6. (5. If fE for some ~) p e ]I, + ~[ , then lim llPyf - fIlp= 0 y~O+ and (5. ~S) Proof. 23) are obvious if tinuous function of compact support.

Due to the facts that f has compact support and gx(t) tends to 0 as Itl ->+~ vals mentioned we shall never need to consider the two infinite inter- above. We define g(x) = ~I J f(t)dt 9 x-c(J) I and gj (x) = ~I J . = j The function J f(t)dt 9 x-c(J) 36 g(x) - gj(x) ffi i f(t)dt 9 x-c(J) Jn J is clearly decreasing in the interval get for x=c(lj) I. 10) we J , g(c(lj)) - gj(c(lj)) > (I-6)X , for x in the left half of I.. I ~m(lj) < m({x I g(x) > 89 ~=i = + n I m({x ] gj(x) < j=l - ~(I-~)}) 2 . llm(lj)< __ 2 11 j =~(--(T~-6)J ~ 2 ~i fJ f(t)dt+ j=l~~ X(I-~) J I.

Download PDF sample

The Carleson-Hunt Theorem on Fourier Series by Ole Groth Jørsboe


by Edward
4.0

Rated 4.61 of 5 – based on 39 votes