臺灣博碩士論文加值系統

我們用震盪積分算子,在一光錐曲面中,以一平面與之相切為零,進而求之衰退速率.

In this paper, we discuss the oscillatory integral operators with
homogeneous polynomial phase functions. The phase function can be
constructed from two polynomials of degree 2. We consider the determinantal polynomials have multiple roots, and we calculate their norms.

Contents
1. Introduction
2. Some Useful Lemmas
3. Main Theorem
4. Remark
References

[1] Shieh-Shun Fu: L2 estimates for oscillatory integral operators and pencils
of homogeneous functions. Forum Math. 11 (1999), 513-541
[2] Greenleaf, A. and G. Uhlmann: Microlocal analysis of the two-plane
transform. Contemporary Mathematics 140 (1992), 65-71
[3] Phong, D. H. and E. M. stein: Oscillatory integrals with polynomial
phases. Invent. Math. 110 (1992), 39-62
[4] Phong, D. H. and E. M. stein: On a Stopping Process for Oscillatory
Integrals. The Journal of Geometric Analysis. Volume 4, Number 1,
1994, 105-120
[5] Christopher Donald. Sogge: Fourier integrals in classical analysis. Cambridge
University Press, 1993, 22
[6] O. Robert and P. Sargos: A general bound for oscillatory integrals with
a polynomial phase of degree k. Math. Res. Lett. 13(2005), no. 4,
531-537
[7] Wan Tang: Decay rates of oscillatory integral operators in ”1+2” dimensions.
Forum Math. 18(2006), 427-444
[8] Phong, D. H. and E. M. stein: Oscillatory integrals with polynomial
phases. Invent. Math. 110 (1992), 332
[9] Phong, D. H. and E. M. stein: Oscillatory integrals with polynomial
phases. Invent. Math. 110 (1992), 329-432
[10] Folland, Gerald B.: Real Analysis: Modern Techniques and Their
Applications (second edition). New York: Wiley, c1999, 67
[11] Michael Ruzhansky: Multidimensional decay in Van der Corput lemma.
[math.AP] 5 Nov (2007).