Access the full text.
Sign up today, get DeepDyve free for 14 days.
References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.
Abstract. In this paper we study oscillatory integral operators, induced from the restricted twoplane transforms, with homogeneous polynomial phases and their L 2 decay estimates. 1991 Mathematics Subject Classi®cation: 58G15, 47G10. 1 Introduction The purpose of this paper is to prove estimates for oscillatory integral operators originating in the study of the two-plane transform. The phase functions of these oscillatory integrals are generic elements in the tensor product space of two homogeà neous polynomials of the same degree k in R m , i.e., R 2 n S k R m . The question of studying such operators was originally posed by Greenleaf and Uhlmann in [6]. Oscillatory integral operators in one variable have been treated by Phong and Stein in [12], [13]. Let MkY n be the space of a½ne k-planes in R n . The k-plane transform RkY n , de®ned by Helgason in [7], is RkY n f p f y dsyY p e MkY n y where f e C0 R n Y ds y is the normalized Lebesgue measure on the k-plane p. RkY n can be extended to E H R n by duality à hRkY n uY gi huY RkY n
Forum Mathematicum – de Gruyter
Published: Aug 1, 1999
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.