Prince Will gets three new titles

Baron Carrickfergus?  Good lord, and bless me.

Martin Beckford in the Telegraph writes that the Queen has bestowed three new titles on her grandon and that Kate Middleton becomes a duchess.
Prince William and Kate Middleton were made the Duke and Duchess of Cambridge on their wedding day, as the Queen bestowed three titles on her grandson.

The Queen conferred the dukedom, the highest rank in the British peerage, on the Prince. He was also given a Scottish title and a Northern Irish one, the Earl of Strathearn and Baron Carrickfergus.
It had been expected that the Prince would become the Duke of Cambridge, but he will hope to avoid the fate of the last holder of the title who became a figure of scandal after marrying a commoner for love.

Now, there's an interesting story.  The ardent fellow in question was Prince George (b. 1819), grandson of mad king George III, and the only son of Prince Adolphus Frederick, the first Duke of Cambridge.  Those were fun, fun, fun times for the blueblooded rich, involving beautiful mistresses.  Prince Georgie became enamoured of an actress, Sarah Louisa Fairbrother -- here pictured as Abdullah in a production called "Open Sesame" -- and desired much to marry her, though she was of dubious reputation, having had two children already.

He was offered an arranged marriage, but stuck to his guns and flatly refused, declaring that arranged marriages were a recipe for disaster (perhaps because he had a glimpse into the distant future).  Parliament or whatever was in charge of such things flatly refused to contemplate a morganatic marriage.  They got wed anyway (Sarah was pregnant) in 1847, but the marriage was never officially recognized.  So Sarah never got to be called the Duchess of Cambridge.  Instead, she was known as Mrs. Fitzgeorge.

Well, to get away from the exciting stuff, how would you address the invitation, if you wanted Kate's company for afternoon tea?

Her Royal Highness The Duchess of Cambridge.
 
Though she may prefer to be called Princess William.