VOLUME 104 NUMBER 1 SEPTEMBER 1988

WHOLE NUMBER 351

Proceedings«A» OF THE

EDITED BY

William AdamsJ. Marshall AshAndreas R. BlassThomas H. BrylawskiDennis BurkeFrederick R. CohenJohn B. ConwayWilliam J. Davis, Managing EditorBarbara L. KeyfitzIrwin Kra

R. Daniel MauldinKenneth R. MeyerPaul S. MuhlyAndrew OdlyzkoGeorge C. Papanicolaou

Donald PassmanLouis J. Ratliff, Jr.Jonathan M. RosenbergWilliam D. SudderthJames E. West

Warren J. Wong

PROVIDENCE, RHODE ISLAND USA

ISSN 0002-9939

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LOGIC AND FOUNDATIONS (03 04)Andreas R. Blass, Department of Mathematics, University of Michigan, Ann Arbor, Michigan

48109-1003COMBINATORICS AND DISCRETE MATHEMATICS (05 15)

Thomas H. Brylawski, Department of Mathematics, University of North Carolina, ChapelHill, North Carolina 27514

COMBINATORICS, COMPUTER SCIENCE AND INFORMATION THEORY (05 68 94)Andrew Odlyzko, Room 2C-370, Bell Laboratories, Murray Hill, New Jersey 07974

COMMUTATIVE ALGEBRA (06 12 13 14 15 18)Louis J. Ratliff, Jr., Department of Mathematics, University of California, Riverside, Califor-

nia 92502GENERAL ALGEBRA (16 17 18 08)

Donald Passman, Department of Mathematics, University of Wisconsin, Madison, Wisconsin53706

GROUP THEORY (20)Warren J. Wong, Department of Mathematics, University of Notre Dame, Notre Dame, Indi-

ana 46556ALGEBRAIC AND DIFFERENTIAL TOPOLOGY (55 57 58)

Frederick R. Cohen, Department of Mathematics, University of Kentucky, Lexington, Ken-

tucky 40506REAL VARIABLES (26 28 40)

R. Daniel Mauldin, Department of Mathematics, North Texas State University, Dentón, Texas

76203COMPLEX VARIABLES (30 31 32)

Irwin Kra, Department of Mathematics, State University of New York at Stony Brook, StonyBrook, New York 11794

NUMBER THEORY (11)William Adams, 11520 Lockhart Place, Silver Spring, Maryland 20902

ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS (33 34 39 49 58)Kenneth R. Meyer, Department of Mathematical Sciences, University of Cincinnati, Cincin-

nati, Ohio 45221-0025PARTIAL DIFFERENTIAL EQUATIONS (35 49)

Barbara L. Keyfitz, Department of Mathematics, University of Houston-University Park,

Houston, Texas 77004GENERAL ANALYSIS (41 42 43 44 45)

J. Marshall Ash, Department of Mathematics, DePaul University, Chicago, Illinois 60614FUNCTIONAL ANALYSIS AND OPERATOR THEORY (46 47)

John B. Conway, Department of Mathematics, Indiana University, Bloomington, Indiana

47405FUNCTIONAL ANALYSIS AND CONVEXITY (46 52)

William J. Davis, Department of Mathematics, Ohio State University, Columbus, Ohio 43210

COMPLEX VARIABLES, FUNCTIONAL ANALYSIS AND OPERATOR THEORY (30 46 47)Paul S. Muhly, Department of Mathematics, University of Iowa, Iowa City, Iowa 52242

LIE GROUPS AND GEOMETRY (22 51 53)Jonathan M. Rosenberg, Department of Mathematics, University of Maryland, College Park,

Maryland 20742GENERAL TOPOLOGY (54)

Dennis Burke, Department of Mathematics, Miami University of Ohio, Oxford, Ohio 45056

James E. West, Department of Mathematics, Cornell University, Ithaca, New York 14853PROBABILITY AND CERTAIN OTHER FIELDS (60-94 inclusive)

William D. Sudderth, Department of Statistics, University of Minnesota, Minneapolis, Min-

nesota 55455George C. Papanicolaou, Applied Mathematics Division, New York University-Courant Insti-

tute, 251 Mercer Street, New York, New York 10012

All other communications should be addressed to the Managing Editor, William J. Davis, atthe above address.

ABCDEFGHIJ-898

CONTENTS— Continued from back cover

An elementary proof of Titchmarsh's convolution theorem. By RAOUF DOSS . 181

An atomic decomposition for parabolic Hv spaces on product domains. By SHUICHI

Sato . 185

Estimates of positive linear operators on Lp. By I. ASSANI . 193

A characterization of discrete Banach lattices with order continuous norms. By WlTOLD

WNUK . 197

Landau's inequality for the difference operator. By MAN KAM KWONG and A. ZETTL. 201

The Kobayashi and Bergman metrics on generalized Thullen domains. By K. T. HAHN

and P. PFLUG. 207

Functions whose derivatives take values in a half-plane. By FERNANDO GRAY and

Stephan Ruscheweyh . 215

Dimension of the graph of Riemann integrable functions. By JAMES FORAN. 219

Inequalities for sums of independent random variables. By N. L. CAROTHERS and S. J.

DlLWORTH . 221

Holder continuity of quasiconformal mappings of the unit ball. By G. D. ANDERSON and

M. K. VAMANAMURTHY. 227

Toeplitz spectral inclusion and generalized in modulus property. By J. JANAS. 231

The derivative of BazileviC functions. By R. R. LONDON and D. K. THOMAS. 235

Ideals of multiplier algebras of simple AF C*-algebras. By HUAXLIN LIN. 239

Covers of non-almost-finite type sofic systems. By SUSAN WILLIAMS. 245

The Schottky problem on pants. By R. C. PENNER. 253

Norms of free operators. By MASSIMO A. PlCARDELLO and TADEUSZ PYTLIK. 257

C. APPLIED MATHEMATICS

Optimal partitioning of a measurable space. By JERZY LEGUT and MACIEJ WlLCZYN-

SKI . 262

D. GEOMETRY

A splitting theorem for 4-dimensional manifolds of nonnegative curvature. By GERARD

WALSCHAP. 265

Covering the boundary of a convex set by tiles. By MAREK LASSAK. 269

Zonoids with minimal volume-product—A new proof. By Y. GORDON, M. MEYER and

S. REISNER. 273

Manifolds of almost half of the maximal volume. By OGUZ C. Durumeric. 277

E. LOGIC AND FOUNDATIONS

Representation of Borel isomorphism by a probability measure. By R. M. SHORTT .... 284

Defining jump classes in the degrees below 0'. By RICHARD A. SHORE . 287

F. STATISTICS AND PROBABILITY

Random nonlinear evolution inclusions in reflexive Banach spaces. By EvGENIOS P.

AVGERINOS and NlKOLAOS S. PAPAGEORGIOU. 293

G. TOPOLOGY

A de Rham type theorem for orbit spaces. By Andrei Verona. 300

Stability of Anosov maps. By JUERGEN QUANDT. 303

Example of a T\ topological space without a Noetherian base. By ANGEL TAMARIZ-

MASCARÚA and RICHARD G. WILSON. 310

Two new topological cardinal inequalities. By SUN SHU-HAO . 313

The space of minimal prime ideals of C(X) need not be basically disconnected. By A.

Dow, M. Henriksen, Ralph Kopperman and J. Vermeer. 317

The inverse limit of the fundamental groups of branched cyclic coverings. By MICHAEL

DELLOMO. 321

Some fibred cobordism groups are not finitely generated. By L. ASTEY, P. GREENBERG,

E. Micha and G. Pastor . 327

The free genus of doubled knots. By CHARLES LIVINGSTON. 329

Corrigendum to "Weak sequential denseness in Banach spaces". By J. HOWARD. 334

CONTENTS

Vol. 104, No. 1 September 1988 Whole No. 351

A. ALGEBRA AND NUMBER THEORY

On gaps between prime numbers. By ADOLF HlLDEBRAND and Helmut MAIER .... 1

Rings with associators in the commutative center. By ERWIN KLEINFELD . 10

Weights of semi-invariants of the quotient division ring of an enveloping algebra. By E.

NAUWELAERTS and A. I. OOMS. 13

Elliptic curves with no rational points. By JIN Nakagawa and KUNIAKI HORIE. 20

Isomorphisms of prime Goldie semiprincipal left ideal rings. By KENNETH G. WOLFSON 25

An application of Baumslag-Solitar nonhopfian groups to finitary automorphisms. By

Francesco Caserta . 30

Simultaneous systems of representatives for finite families of finite sets. By XlNG-DE JIA 33

A characterization of artinian rings whose endomorphism rings have finite global dimension.

By Dan Zacharia. 37

The isomorphism question for modular group algebras of metacyclic p-groups. By CZE-

SLAW BAGIÑSKI . 39

Leopoldt's conjecture in parameterized families. By JOHANNES BUCHMANN and JONA-

THAN W. Sands. 43

Noncommutative regular local rings of dimension 3. By ROBERT L. SNIDER. 49

Order relation in quadratic Jordan rings and a structure theorem. By SANTOS GONZALEZ

and CONSEUELO MARTÍNEZ. 51

Kida's theorem for a class of nonnormal extensions. By ROBERT GOLD and MANOHAR

MADAN . 55

The Hodge group of an abelian variety. By V. KUMAR MURTY. 61

B. ANALYSIS

The dominated ergodic estimate for mean bounded, invertible, positive operators. By

F. J. MARTIN-REYES and A. DE LA TORRE . 69

Fréchet differentiate points in Bochner function spaces Lp(p.,X). By WANG Jian-Hua

and NAN CHAO-XUN . 76

A range theorem for the Radon transform. By W. R. MADYCH and D. C. SOLMON ... 79

Singular measures with spectral gaps. By RUSSELL LYONS. 86

The regularity of Dunford-Pettis operators. By JAMES R. HOLUB. 89

Some applications of selection theorems to parametrization problems. By A. MAITRA,

B. V. Rao and V. V. Srivatsa. 96

A Banach space on which there are few operators. By SAHARON SHELAH and JURIS

STEPRÄNS . 101

Generalized open mapping theorems for bilinear maps, with an application to operator

algebras. By P. G. DlXON.{. 106

Uniformly persistent semidynamical systems. By ALESSANDRO FONDA. Ill

Subaveraging estimates for CR functions. By A. BOGGESS and R. DWILEWICZ. 117

The initial value problem for a degenerate wave equation. By Y. KANNAI and S. KlRO. 125

A factorization theorem for unfoldings of analytic functions. By TATSUO SUWA. 131

The integrability of generalized Garrett-Stanojevié sums. By NlRANJAN SlNGH and

K. M. Sharma .'.. 135

Complex retractions and envelopes of holomorphy. By S. TRAPANI. 145

Exponential dichotomies and Fredholm operators. By Kenneth J. PALMER. 149

Mazur's intersection property and a Krein-Milrnan type theorem for almost all closed, con-

vex and bounded subsets of a Banach space. By PANDO GriGOROV Georgiev 157

Lp continuity of pseudo-differential operators with discontinuous symbol. By J. Alvarez

and R. DURAN. 165

Radial symmetry of the first eigenfunction for the p-Laplacian in the ball. By TlLAK

Bhattacharya. 169

Fourth-order two-point boundary value problems. By YlSONG YANG. 175

(Continued on inside back cover)