Empyrean

This 10-minute organ recital piece was composed in 1981-2 for the Lloyd's Bank / Cornhill National Composition Competition, in which it won both the First Prize and the Special Prize for an unpublished composer aged under 30. Inspired by the experience of sitting under the Octagon of Ely Cathedral during a performance of Berlioz's Grande Messe des Morts, the music bears a superscription in the form of the first and last verses from one of the great hymn texts of Isaac Watts (1674-1748): 'Give us the wings of faith, to rise Within the veil, and see The saints above, how great their joys, How bright their glories be... ...Our glorious Leader claims our praise For His own pattern given, While the great cloud of witnesses Show the same path to heaven.' The composer's note for this work may be read below as a scanned upload. Two separate commercial recordings of this work were released during 2015 and are detailed below. An earlier recording was released by the then Assistant Organist of Christ Church Cathedral Dublin, Tristan Russcher, in 2006

A sufficient condition for the boundedness of operator-weighted martingale transforms and Hilbert transform

Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space H. We show that if W and its inverse W−1 both satisfy a matrix reverse Holder property introduced in [2], then the weighted Hilbert transform H : L2W(R,H) → L2W(R,H) and also all weighted dyadic martingale transforms Tσ: L2W(R,H) → L2W(R,H) are bounded. We also show that this condition is not necessary for the boundedness of the weighted Hilbert transform

Christus

Passion Symphony for organ solo in five movements. Large-scale work lasting 2 hrs and 05 mins., intended for recital use linked to the liturgy of the Church year

'If I were going there, I wouldn't start from here'

A composer reflects on the perils of getting one's bearings in a new piece

When David heard that Absalom was slain

Motet for double chorus a cappella, commissioned by the St Louis Chamber chorus in 2008 and receiving its world premiere from that ensemble under the direction of Philip Barnes, Christ Church Cathedral, St Louis, Missouri, USA, 2008. The work is due for eventual publication by Edition Peters under terms of its contract with the composer. Subsequent UK performances of the motet by the Vasari Singers under Jeremy Backhouse (Bath Abbey and other) preceded their CD global release of the work on the Naxos label. Duration: ca 9’30”. The following note appears on the composer's website: This work was commissioned for the St Louis Chamber Chorus by John and Gailya Barker in memory of their parents. Its première took place within a programme conceived on the theme of Winchester Cathedral, with which Christ Church Cathedral in St Louis has special links (an inscribed stone from Winchester Cathedral is set into one of its walls and its reredos is a copy of the 19th century original at Winchester). The choice of text was made in order to juxtapose this new setting by a recent member of Winchester Cathedral Choir to the much earlier one by Thomas Weelkes, Organist at Winchester College for a few years beginning in 1598 (and subsequently Organist at Chichester Cathedral). This modern setting attempts to respond to the timeless grief of a parent mourning his or her child, and to bring this sympathetically into line with resonances of a contemporary world where such private grief is all too frequently brought to universal attention through intrusive coverage by news media. At the same time, the music seeks to respect the aesthetic and technique of the setting by Weelkes -and also that by Thomas Tomkins, prized yet more highly by the present composer. (Tribute should be paid here also to the fine contemporary setting by Jonathan Rathbone.

Bounds for Calder\'on-Zygmund operators with matrix A2A_2 weights

It is well-known that dyadic martingale transforms are a good model for Calder\'on-Zygmund singular integral operators. In this paper we extend some results on weighted norm inequalities to vector-valued functions. We prove that, if $W$ is an $A_2$ matrix weight, then the weighted $L^2$-norm of a Calder\'on-Zygmund operator with cancellation has the same dependence on the $A_2$ characteristic of $W$ as the weighted $L^2$-norm of the martingale transform. Thus the question of the dependence of the norm of matrix-weighted Calder\'on-Zygmund operators on the $A_2$ characteristic of the weight is reduced to the case of dyadic martingales and paraproducts. We also show a slightly different proof for the special case of Calder\'on-Zygmund operators with even kernel. We conclude the paper by proving a version of the matrix-weighted Carleson Embedding Theorem. Our method uses the Bellman function technique to obtain the right estimates for the norm of dyadic Haar shift operators. We then apply the representation theorem of T. Hyt\"onen to extend the result to general Calder\'on-Zygmund operators.Comment: arXiv admin note: text overlap with arXiv:1310.786

Logarithmic mean oscillation on the polydisc, endpoint results for multi-parameter paraproducts, and commutators on BMO

We study boundedness properties of a class of multiparameter paraproducts on the dual space of the dyadic Hardy space H_d^1(T^N), the dyadic product BMO space BMO_d(T^N). For this, we introduce a notion of logarithmic mean oscillation on the polydisc. We also obtain a result on the boundedness of iterated commutators on BMO([0,1]^2).Comment: 24 page