*Editors*: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao (Houston),
H. Brezis (Paris), J. Damon (Chapel Hill), K. Davidson (Waterloo), C. Hagopian
(Sacramento), R. M. Hardt (Rice), J. Hausen (Houston), J. A. Johnson (Houston),
J. Nagata (Osaka), B. H. Neumann (Canberra), G. Pisier (College Station and
Paris), S. W. Semmes (Rice)
*Managing Editor*: K. Kaiser (Houston)

*Contents*

**Youngho Jang ** and **Hoil Kim**, T.G.R.C., Kyungpook National
University, Taegu 702-701, Korea, (janggane@chollian.net),
(hikim@gauss.kyungpook.ac.kr).
* A series whose terms are
products of two q-Bernoulli Numbers in the p-adic Case,*
pp. 495--510.

ABSTRACT. The symmetric property A

**Alireza Abdollahi, **Department of Mathematics, University of Isfahan,
Isfahan 81744, Iran, (abdolahi@math.ui.ac.ir).

Some Engel Conditions on
Finite Subsets of Certain Groups, pp. 511-522.

ABSTRACT.
Engel-like conditions with respect to nilpotency of groups are studied.

**Keith Whittington,** Department of Mathematics, University of the
Pacific, Stockton, CA 95211, (kwhittin@uop.edu).

Open Connected Sets in
Homogeneous Spaces, pp. 523-531.

ABSTRACT.
It is shown that if a polish topological group acts transitively on a locally
compact polish space, then for "most" pairs of points in the space, every
continuum containing these points (if any) has arbitrarily small open connected
neighborhoods. Characterizations are then given of local connectedness.

**Louis Zulli,** Department of Mathematics, Lafayette College, Easton, PA
18042-1781, (zullil@lafayette.edu)

Seifert 3-Manifolds that are
Bundles and Semi-Bundles, pp. 533-540.

ABSTRACT.
We identify the closed, connected, orientable Seifert 3-manifolds that are both
surface bundles over the circle and semi-bundles---unions of twisted I-bundles
over non-orientable surfaces. We show that there is a single infinite family
(indexed by the integers) of closed, connected, oriented Seifert 3-manifolds
that admit both structures.

** Seokku Ko .** Konkuk University, Choongjusi Choongbuk, Korea 380-701.
(seokko@apmath.kku.edu),
(seokko@kku.ac.kr).

Embedding Compact Riemann Surfaces
in Riemannian Manifolds, pp. 541-577.

ABSTRACT.
Any compact Riemann surface has a conformal model in any orientable Riemannian
manifold. Precisely, we will prove that, given any compact Riemann surface,
there is a conformally equivalent model in a prespecified orientable Riemannian
manifold. The techniques we use include Garsia's Continuity Lemma, Brouwer's
Fixed Point Theorem along with techniques from Teichmuller theory.

**C. E. Gutierrez,** Department of Mathematics,Temple University,
Philadelphia, PA 19122 (gutierrez@math.temple.ed), **A. Incognito, ** School
of Science and Engineering, Al Akhawayn University in Ifrane, Ifrane, Morocco
53000, P.O. Box 1862 (A.Incognito@alakhawayn.ma) and **J. L. Torrea, **
Departamento de Matematicas, Universidad Autonoma de Madrid, Cantoblanco, 28049
Madrid, Spain (joseluis.torrea@uam.es).

Riesz Transforms,
g-Functions, and Multipliers for the Laguerre Semigroup, pp. 579-592.

ABSTRACT.
We study a version of Riesz transforms and show that they are bounded in L^{p}
spaces.

**Dutrieux, Yves, ** Université Pierre et Marie Curie, Paris 6, Boite 186, 4
place Jussieu, 75252 Paris Cedex 05, France
(dutrieux@ccr.moka.jussieu.fr).

Quotients of
** c _{0}** and Lipschitz-homeomorphisms, pp. 593-599.

ABSTRACT. In this paper it is shown that a Banach space whose dual has the approximation property and which is Lipschitz homeomorphic to a quotient of c

**C. E. M. Pearce, **Applied Mathematics Dept, The University of Adelaide,
Adelaide, SA 5005, Australia (cpearce@maths.adelaide.edu.au), **J. Pevcaric, **
Applied Mathematics Dept, The University of Adelaide, Adelaide, SA 5005,
Australia (jpecaric@maths.adelaide.edu.au), and **S. Varovsanec, **
Department of Mathematics, The University of Zagreb, 10000 Zagreb, Croatia
(varosans@math.hr).

Polya--type Inequalities for Arbitrary Functions, pp. 601-612.

ABSTRACT.
Generalizations of the Polya integral inequality for nonnegative, nondecreasing
functions are given involving real and operator functions which satisfy certain
subordination and boundary conditions but are otherwise arbitrary. Both discrete
and integral versions of the results are addressed. Applications are made to
generalized quasiarithmetic means, symmetric means and to operator means.

**M. Nakamura, **Graduate School of Information Sciences(GSIS), Tohoku
University, Sendai 980-8577, Japan
(m-nakamu@math.is.tohoku.ac.jp) and **T. Ozawa, **
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan.

Small Solutions to Nonlinear Wave Equations in the Sobolev Spaces, pp.
613-632.

ABSTRACT.
The local and global well-posedness for the Cauchy problem for a class of
nonlinear wave equations is studied. The global well-posedness of the problem is
proved in the homogeneous Sobolev space H^{s} of fractional order s>n/2
under the following assumptions: (1) The norm of the Cauchy data in H^{1/2}
is relatively small with respect to the norm in H^{a}
for any fixed a with n/2< a< s. (2) The nonlinearity, f(u), behaves as a power
of 1+4/(n-1) near zero and has an arbitrary growth rate at infinity.

**Leszek Skrzypczak, **Faculty of Mathematics and Computer Science,
A.Mickiewicz University Matejki 48-49 60-769 Poznan, Poland (lskrzyp@amu.edu.pl)
and **Bernadeta Tomasz, ** Faculty of Mathematics and Computer Science,
A.Mickiewicz University Matejki 48-49 60-769 Poznan, Poland (betom@amu.edu.pl).

Compactness of Embeddings of the Trudinger-Strichartz Type for Rotation
Invariant Functions, pp. 633-647.

ABSTRACT.
Let H be a close subgroup of the group O(n) of rotations of the n-dimensional
Euclidean space. Subspaces of functions of fractional Sobolev spaces and the
Besov spaces invariant with respect to the natural action of the group H are
investigated. Sufficient and necessary conditions for the compactness of the
Trudinger-Strichartz type embeddings of the above subspaces into the
``exponential'' Orlicz classes are given. In particular it is proved that the
compactness implies that any orbit of the action of the group H on the unit
sphere is infinite.

**Marino Badiale, **Scuola Normale Superiore, Piazza dei Cavalieri 7,
I-56126 Pisa Italy (badiale@bibsns.sns.it) and **Alessandro Duci, **Scuola
Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa Italy (duci@cibs.sns).

Concentrated Solutions for a Non Variational Semilinear Elliptic Equation ,
pp. 649-682.

ABSTRACT.
We study a non-variational semilinear elliptic equation and use a reduction
method for perturbation problems and find solutions that look like spikes
concentrated near suitable points.

**Annalisa Baldi, **Dipartimento di Matematica, Universita di Bologna,
Piazza di Porta S. Donato, 5, I-40127 Bologna, Italy (baldi@dm.unibo.it)

Weighted BV Functions , pp. 683-705.

ABSTRACT.
We provide a definition of weighted function of bounded variation when the
weight function `\omega` belongs to a certain subclass of Muckenhoupt's A_{1}
weight class. We obtain Poincaré and isoperimetric inequalities in this space
and, as an application, we prove existence of minimal surfaces.

**Young-Bok Chung, **Department of Mathematics, Chonnam National
University, Kwangju 500-757, Korea (ybchung@chonnam.chonnam.ac.kr).

Higher Order Extremal Problem and Proper Holomorphic Mapping , pp. 707-718.

ABSTRACT.
Higher order problems with respect to the Riemann mapping theorem are studied.