Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 1
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Carton-Lebrun, C. and Heinig, H. P. 1992. Weighted Fourier Transform Inequalities for Radially Decreasing Functions. SIAM Journal on Mathematical Analysis, Vol. 23, Issue. 3, p. 785.
    ×
  • Get access
    Add to cart USD35.00
    Check if you have access via personal or institutional login
    Log in Register Recommend to librarian

Weighted norm inequalities for the Hankel- and -transformations

  • S. A. Emara (a1) and H. P. Heinig (a1)
Synopsis

We give conditions on pairs of non-negative weight functions u and v which are sufficient that, for 1<p, q <∞,

where T is the Hankel-or the K-transformation.

The proofs are based on a weighted Marcinkiewicz interpolation theorem for linear operators. In the case that T is the Hankel transformation and 1<p≦q <∞, the result is similar to a weighted estimate of Heywood and Rooney [9], but with different weight conditions.

Copyright
COPYRIGHT: © Royal Society of Edinburgh 1986
References
Hide All
1Benedetto, J. J., Heinig, H. P. and Johnson, R.. Weighted Hardy spaces and the Laplace transform II. Math. Nachr. (to appear).
2Calderón, A. P.. Spaces between L1 and L∞ and the theorem of Marcinkiewicz. Studio Math. 26 (1966), 273–299.
3Erdelyi, A. (ed.). Tables of integral transforms, Vol. II (New York: McGraw Hill, 1954).
4Gradshteyn, I. G. and Ryzhik, I. M.. Tables of Integrals, Series and Products (New York: Academic Press, 1980).
5Hardy, G. H., Littlewood, J. E. and Polya, G.. Inequalities (Cambridge University Press, 1952).
6Heinig, Hans P.. Weighted norm inequalities for classes of operators. Indiana Univ. Math. J. 33 (1984), 573–582.
7Heinig, Hans P.. Estimates for operators in mixed weighted Lp-spaces. Trans. Amer. Math. Soc. 287 (1985), 483–493.
8Heinig, Hans P.. Weighted norm inequalities for certain integral operators II. Proc. Amer. Math. Soc. 95 (3) (1985), 387–396.
9Heywood, P. and Rooney, P. G.. A weighted norm inequality for the Hankel transformation. Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 45–50.
10Mazja, Wladimir. Einbettungssätze fur Sobolevsche Räume, Teil 1. Teubner Texte zur Math (Leipzig: Teubner, 1979).
11Muckenhoupt, B.. A note on the two weight function condition for the Fourier transform norm inequality. Proc. Amer. Math. Soc. 88 (1983), 97–100.
12Muckenhoupt, B.. Weighted norm inequalities for the Fourier transform. Trans. Amer. Math. Soc. 276 (1983), 729–742.
13Schwartz, Laurent. Mathematics for the Physical Sciences (Paris: Herman, 1966).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 4 *
Loading metrics...

Abstract views

Total abstract views: 68 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×