Actually, "more importantly" is quite correct. Here's part of an explanation from The Oxford Dictionary of American Usage and Style*:
"As an introductory phrase, more important has historically been considered an elliptical form of ˜What is more important....,' and hence the -ly form is sometimes thought to be less desirable. Yet, three points militate against this position... "
His first point is the most important. He notes that since we may begin a sentence with importantly, as in "Importantly, the production appeared first off-Broadway....," we ought to be able to begin it moreimportantly. This use of importantly is as a sentence adverb, which qualifies an entire statement rather than a single word in the sentence. The sentence does not correspond itself into the form "in a XXXX manner," as adverbs also do. So, in:
Happily, the bill did not go beyond the committee, the introductory adverb happily conveys the writer's opinion on the message being imparted, not the idea that the bill happily went or did not go beyond the committee.
Here are some other sentence adverbs ending in –ly that appear frequently:
"Improvising sentence adverbs from traditional adverbs like hopefully (=in a hopeful manner) and thankfully (= in a thankful manner) is objectionable to many stylists but seems to be on the rise....And in formal prose, hopefully and thankfully shouldn't appear. Though increasingly common, they have a tarnished history." ______
Here are some adverbs used as sentence modifiers:
Frankly, my dear, I don't give a damn.
Oddly enough, the postal service delivered the mail on time even though many roads were closed due to the heavy snowstorm.
Regrettably, I lent him four thousand dollars, and more regrettably, he has left the country without a forwarding address.
Importantly, the voters are becoming aware of the corruption, and more importantly, they are going to vote against the incumbent. _____
So, even though "more importantly" can be defended logically, in order to avoid problems, you might want to use another phrase: either "what is more important" or just "more important," both of which are also correct.
Rachel _______ *The Oxford Dictionary of American Usage and Style by Bryan A. Garner. Oxford University Press. 2000
In the new edition of his book, Garner also adds an interesting point as follows:
"The criticism of more importantly and most importantly has always been rather muted and obscure, and today it has dwindled to something less than muted and obscure. So writers needn't fear any criticism for using the -ly forms; if they encounter any, it's easily dismissed as picayunish pedantry."
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