Who holds Vivaldi's music rights? How can I research the same info. for other classical composers?

I want to know if their music is considered "royalty-free" or if you musp pay to use it in publications or with comercial ends.

The compositions are public domain i.e royalty free but any recording made will be copyrighted by the recording artists/studio etc. Therefore you cannot use, for Example, a work which has been performed by the London Symphony Orchestra with impunity from royalties.

Copyright restrictions generally only persist past the life of the original creator for a period of 70 years at most (so the creator's children and grandchildren may claim exclusive rights), so by now all of Vivaldi's works are in the public domain. However, in order to perform Vivaldi's works royalty-free, you will need to obtain access to the original works and prepare your own editions. If you don't want to do that, you'll have to obtain any of the various published editions. Since the publishers have added to the body of work by editing them (e.g. for modern notation, readability, correction of obvious flaws in the manuscript, etc), the publishers retain a copyright of specific editions. You'll have to pay a licensing fee to the publisher to perform their edition of the works.

The two above answers are perfectly correct, and I would only add two points. The copyright in recordings ceases after 50 years - which is why various labels are now issuing CDs of things like the EMI back catalogue from the 50s. However, I would guess that rights will be claimed in the remastering. The edition point made by dansinge was emphasised a few years ago (here in the UK) when a very reputable record company issued a work by CPE Bach without paying fees to the learned professor who had made some editorial amendments. There was a lengthy legal battle and the prof. won, landing Hyperion Records with an very hefty legal bill which nearly finished the company (but fortunately didn't)

The above answers are correct EXCEPT ...

Copywrite laws in the US were changed so that it is 95 years, not 70. Also, other countries have different laws with different time frames.

BUT to be sure, Vivaldi is DEFFINATELY in the public domain. You can play, perform, record, and sell any of his music - but you can not reproduce, broadcast, or otherwise legally sell or transmit SOMEONE ELSE'S recording of his work without their expressed permission.