Lectures given at DePaul University ,
Chicago, Illinois, July 14-18, 1986
Supported by the Conference Boar d
of the Mathematical Science s
Research supporte d by National Scienc e Foundation Gran t DMS-8602950 .
1980 Mathematics Subject Classifications (1985 Revision). 60G44 , 26D15
26B15, 44A15, 47D05, 60J05, 60J25.
Library of Congress Cataloging-in-Publication Dat a
Some topics in probability an d analysis / Richar d F . Gundy,
p. cm. —(Conference Boar d of the Mathematical Science s
Regional conference serie s in mathematics; no. 70.)
Bibliography: p .
ISBN 0-8218-0721-8 (alk . paper)
1. Inequalities (Mathematics ) 2 . Harmonic functions. I . Series: Regiona l
conference serie s in mathematics; no. 70.
QA1.R33 no . 70 [Q A 295] 510 s—dcl9 [512.9'7] 89-30 3 CIP
Copying and reprinting. Individua l reader s o f thi s publication , an d nonprofi t librarie s actin g fo
them, ar e permitte d t o mak e fai r us e o f th e material , suc h a s to cop y a n articl e fo r us e in teachin g o
research. Permissio n i s granted t o quot e brie f passage s fro m thi s publicatio n i n reviews , provide d th
customary acknowledgmen t o f the source is given.
Republication, systemati c copying, or multiple reproduction o f any material in this publication (in
cluding abstracts) i s permitted only under license from th e American Mathematical Society. Request s fo
such permission should be addressed to the Executive Director, American Mathematical Society, P.O. Bo
6248, Providence, Rhode Island 02940.
The owner consents to copying beyond that permitted by Sections 107 or 108 of the U.S. Copyrigh
Law, provide d tha t a fe e o f $1.00 plu s $.2 5 pe r pag e fo r eac h cop y b e pai d directl y t o th e Copyrigh
Clearance Center , Inc. , 2 1 Congres s Street , Salem , Massachusett s 01970. Whe n payin g thi s fe e pleas
use the cod e 0160-7642/89 t o refe r t o this publication. Thi s consent doe s not exten d t o other kind s o
copying, such as copying for general distribution, for advertising or promotion purposes, for creating ne
collective works, or for resale.
Copyright ©1989 b y the American Mathematica l Society . Al l rights reserved.
Printed i n the United State s of America
The American Mathematica l Societ y retains all rights
except those granted to the United State s Government .
The paper used in this book is acid-free an d falls within the guidelines
established to ensure permanence and durability. @