Downloads #a { width: 402px; height: 117px; } @media only screen and (max-device-width: 720px) { #a { width: 134px; height: 39px; } } Most of my papers and preprints are below, plus two book extracts. Hyperlinks point to stable open access downloads if they exist, or else to preprints.

#### Preprints

1. Commuting probabilities of quasigroups, preprint.

2. Distributive algebras, isoclinism, and invariant probabilities, preprint.

3. Degree sum deficiency in finite groups, preprint (with D. MacHale and Á. Ní Shé).

4. Groups with commuting probability 1/3, preprint (with D. MacHale).

5. Finite rings with many idempotents, preprint (with D. MacHale).

6. Odd order rings with many idempotents, preprint (with D. MacHale).

7. Finite rings with many commuting pairs of elements, preprint (with D. MacHale and Á. Ní Shé).

8. Contrasting the commuting probabilities of groups and rings, preprint (with D. MacHale).

9. Isoclinism and weak isoclinism invariants, preprint.

10. Polynomial product semigroups and ring commutativity, preprint (with Yu. Zelenyuk).

11. Wiring switches to lightbulbs, preprint (with A.G. O'Farrell).

#### Books and course notes

1. Codaigh agus Córais Dhinimiciúla Réadacha, Logic Press, 2006.

2. Fractals and Real Dynamical Systems, Logic Press, 2006.

3. Sobolev spaces: a short course, presented in Universidad de La Laguna, May 2000.

#### Papers: Algebra

1. Rings with ideal centres, Sci. Math. Jpn., to appear (with D. MacHale).

2. A characterization of commutator-forcing polynomials, Math. Proc. R. Ir. Acad., to appear (with D. MacHale).

3. Finite rings with large anticommuting probability, Appl. Math. Inf. Sci. 8 (2014), 13–25 (with D. MacHale and Yu. Zelenyuk).
Preprint     Reprint: Journal site

4. Minimal order semigroups with specified commuting probability, Semigroup Forum (2013).
Preprint     Reprint: Journal site

5. Conjugate deficiency in finite groups, Bull. Irish Math. Soc. 71 (2013), 13–19 (with D. MacHale).
Reprint: Journal site

6. Variations on a theme: rings satisfying $$x^3=x$$ are commutative, Amer. Math. Monthly 120 (2013), 430–440 (with D. MacHale).

7. Polynomials that force a unital ring to be commutative, Results Math. 64 (2013) 59–65 (with D. MacHale).
Preprint     Reprint: Journal site

8. Z-polynomials and ring commutativity, Math. Proc. R. Ir. Acad. 112 (2012), 51–57 (with D. MacHale).

9. Small rings without ideal centres, Bull. Irish Math. Soc. 70 (2012), 41–49 (with D. MacHale).
Reprint: Journal site

10. Powers of commutators and anticommutators, ISRN Algebra, vol. 2012, Article ID 302524 (2012), 1–6 (with D. MacHale).
Reprint: Journal site

11. Centrifiers and ring commutativity, J. Math. Sci. Adv. Appl. 15 (2012),139–161 (with D. MacHale).

12. Noncommutative anticommutative rings, Bull. Irish Math. Soc. 18 (1987), 55–57 (with D. MacHale).

13. Dividing an angle into equal parts, Math. Gaz. 69 (1985), 9–12 (with D. MacHale).

14. A note on the ring axioms, Math. Gaz. 68 (1984), 215–216.

#### Papers: Analysis

1. Iterated log-scale Orlicz-Hardy inequalities, Ann. Acad. Sci. Fenn. Math. 38 (2013), 757–770 (with R. Hurri-Syrjänen).
Reprint: Journal site

2. Best constants for metric space inversion inequalities, Cent. Eur. J. Math. 11 (2013), 865–875 (with S. Hamza).
Preprint      Reprint: Journal site

3. Distinguishing properties of weak slice conditions II, Int. J. Pure Appl. Math. 71 (2011), 83–98 (with A. Diatta and A. Stanoyevitch).
Reprint: Journal site

4. Nonpositive curvature and complex analysis, Contemporary Math. 525 (2010), 43–83.

5. Univalent interpolation in Besov spaces and superposition into Bergman spaces, Potential Anal. 29 (2008), 1–16 (with D. Vukotic).

6. Metric space inversions, quasihyperbolic distance, and uniform spaces, Indiana U. Math. J. 57 (2008), 837–890 (with D. Herron and X. Xie).

7. Uniform domains and weak slice spaces, Conform. Geom. Dyn. 11 (2007), 191–206 (with D. Herron).

8. Uniform domains and capacity, Israel J. Math., 158 (2007), 129–157 (with D. Herron).

9. Ends of metric measure spaces and Sobolev inequalities, Math. Z. 252 (2006), 275–285 (with P. Koskela).

10. Superposition operators and the order and type of entire functions, Contemp. Math. 393 (2006), 51–58 (with D. Vukotic).

11. Admissable measures in one dimension, Proc. Amer. Math. Soc. 134 (2006), 703–705 (with J. Björn and S. Keith).
Reprint: Journal site     Review: MR 2180887 (2006k:26021)

12. Sphericalization and flattening, Conform. Geom. Dyn. 9 (2005), 76–101 (with Z. Balogh).
Reprint: Journal site     Review: MR 2179368 (2006k:30046)

13. Relative solidity for spaces of holomorphic functions, Math. Proc. R. Ir. Acad. 104A (2004), 83–97.

14. Orlicz-Hardy inequalities, Illinois J. Math. 48 (2004), 787–802 (with P. Koskela).

15. Quasiconformal images of Hölder domains, Ann. Acad. Sci. Fenn. Math. 29 (2004), 21–42.
Reprint: Journal site     Review: MR 2041697 (2004m:30030)

16. Slice conditions and their applications, Rep. Univ. Jyväskylä Dept. Math. Stat. 92 (2003), 63–76.

17. Distinguishing properties of weak slice conditions, Conform. Geom. Dyn. 7 (2003), 49–75 (with A. Stanoyevitch).
Reprint: Journal site     Review: MR 1992037 (2004f:30014)

18. Superposition operators on Dirichlet type spaces, Report. Univ. Jyväskylä Dept. Math. Stat. 83 (2001), 41–61 (with J.L. Fernández and D. Vukotic).
Reprint: Journal site     Review: MR 1886612 (2002m:30066)

19. Weak slice conditions and Hölder imbeddings, J. London Math. Soc., 66 (2001), 690–706 (with A. Stanoyevitch).

20. Weak slice conditions, product domains, and quasiconformal mappings, Rev. Mat. Iberoam., 17 (2001), 1–37 (with A. Stanoyevitch).

21. Doubling for general sets, Math. Scand. 88 (2001), 229–245 (with P. MacManus and B. Hanson).
Reprint: Journal site      Review: MR 1839574 (2002k:26004)

22. Mixed norms and analytic function spaces, Proc. R. Ir. Acad. 100A (2000), 1–9.

23. Singular measures and the key of G, Publ. Mat. 44 (2000), 483–489 (with P. MacManus).
Reprint: Journal site     Review: MR 1800819 (2001h:60069)

24. Inequalities of John-Nirenberg type in doubling spaces, J. Analyse Math. 79 (1999), 215–240.

25. Is the maximal function of a Lipschitz function continuous?, Ann. Acad. Sci. Fenn. 24 (1999), 519–528.
Reprint: Journal site     Review: MR 1724375 (2001e:42025)

26. Weighted Trudinger-type inequalities, Indiana Univ. Math. J. 48 (1999), 85–114 (with J. O'Shea).

27. On the fusion problem for degenerate elliptic equations II, Comment. Math. Univ. Carolin. 40 (1999), 1–6 (with P. Koskela).
Reprint: Journal site     Review: MR 1715198 (2000j:435078)

28. Bounded and compact multipliers between Bergman and Hardy spaces, Integr. Equ. Oper. Theory 35 (1999), 1–19 (with M.S. Ramanujan and D. Vukotic).

29. Fractional integration, differentiation, and weighted Bergman spaces, Math. Proc. Cambridge Phil. Soc. 126 (1999), 369-385 (with P. Koskela and D. Vukotic).

30. Strong doubling conditions, Math. Ineq. Appl. 1 (1998), 533–542.

31. New Poincaré inequalities from old, Ann. Acad. Sci. Fenn. 23 (1998), 251–260 (with P. Koskela).
Reprint: Journal site     Review: MR 1601883 (99a:46057)

32. Sequences of reverse Minkowski type, Proc. R. Ir. Acad. 96A (1996), 147–157.

33. Boman equals John, Proc. XVI Rolf Nevanlinna Colloquium (1996), 91–99 (with P. Koskela and G. Lu).

34. Criteria for imbeddings of Sobolev-Poincaré type , Internat. Math. Res. Not. 18 (1996), 881–902 (with P. Koskela).

35. Space-filling curves and related functions, Bull. Irish Math. Soc. 36 (1996), 9–18.

36. Pointwise multipliers for reverse Hölder spaces II, Proc. R. Ir. Acad. 95A (1995), 193–204.

37. Subelliptic Poincaré inequalities: the case $$p<1$$, Publ. Mat. 39 (1995), 313–334 (with P. Koskela and G. Lu).
Reprint: Journal site     Review: MR 1370889 (97d:35028)

38. Sobolev-Poincaré implies John, Math. Research Letters 2 (1995), 577–594 (with P. Koskela).

39. Sobolev-Poincaré inequalities for $$p<1$$, Indiana Univ. Math. J. 43 (1994), 221–240 (with P. Koskela).

40. Pointwise multipliers for reverse Hölder spaces, Studia Math. 109 (1994), 23–39.

41. Summation conditions on weights, Michigan Math. J. 40 (1993), 153–170.
Reprint: http://dx.doi.org/10.1307/mmj/1029004679 (Project Euclid)     Review: MR 1214060 (94d:42021)

42. Estimates for operator norms on weighted spaces and reverse Jensen inequalities, Trans. Amer. Math. Soc. 340 (1993), 253–272.

#### Papers: Geometry

1. The boundary at infinity of a rough CAT(0) space, Anal. Geom. Metric Spaces, to appear (with K. Falk).

2. Natural maps between CAT(0) boundaries, New York J. Math. 19 (2013), 13–22 (with K. Falk).
Reprint: Journal site

3. The $$n$$-point condition and rough CAT(0), Anal. Geom. Metric Spaces 1 (2012), 58-68 (with B. Hanson).
Reprint: Journal site

4. Rough CAT(0) spaces, Bull. Math. Soc. Sci. Math. Roumanie 55 (103) (2012), 3–33 (with K. Falk).
Reprint: Journal site

5. The spherical boundary and volume growth, ISRN Geometry, vol. 2012, Art. ID 484312 (2012), 1–13 (with S. Kokkendorff).
Reprint: Journal site

6. On Ptolemaic metric simplicial complexes, Math. Proc. Cambridge Phil. Soc. 149 (2010), 93–104 (with J. McDougall and D.J. Wraith).

7. Ptolemaic spaces and CAT(0), Glasgow Math. J. 51 (2009), 301–314 (with K. Falk and D.J. Wraith).

8. Comparing the Floyd and ideal boundaries of a metric space, Trans. Amer. Math. Soc. 361 (2009), 715–734 (with S.L. Kokkendorff).

9. Detours and Gromov hyperbolicity, Int. J. Pure Appl. Math. 47 (2008), 313–323 (with S.L. Kokkendorff).
Reprint: Journal site

10. Warped products and conformal boundaries of CAT(0) spaces J. Geom. Anal. 18 (2008), 704–719 (with S.L. Kokkendorff).

11. Geometric characterizations of Gromov hyperbolicity, Invent. Math. 153 (2003), 261–301 (with Z. Balogh).