# Oscillatory kernels in certain Hardy-type spaces

Studia Mathematica (1994)

- Volume: 111, Issue: 2, page 195-206
- ISSN: 0039-3223

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topChen, Lung-Kee, and Fan, Dashan. "Oscillatory kernels in certain Hardy-type spaces." Studia Mathematica 111.2 (1994): 195-206. <http://eudml.org/doc/216128>.

@article{Chen1994,

abstract = {We consider a convolution operator Tf = p.v. Ω ⁎ f with $Ω(x) = K(x)e^\{ih(x)\}$, where K(x) is an (n,β) kernel near the origin and an (α,β), α ≥ n, kernel away from the origin; h(x) is a real-valued $C^∞$ function on $ℝ^n ∖ \{0\}$. We give a criterion for such an operator to be bounded from the space $H^\{p\}_\{0\}(ℝ^n)$ into itself.},

author = {Chen, Lung-Kee, Fan, Dashan},

journal = {Studia Mathematica},

keywords = {Hardy-type spaces; oscillating integrals},

language = {eng},

number = {2},

pages = {195-206},

title = {Oscillatory kernels in certain Hardy-type spaces},

url = {http://eudml.org/doc/216128},

volume = {111},

year = {1994},

}

TY - JOUR

AU - Chen, Lung-Kee

AU - Fan, Dashan

TI - Oscillatory kernels in certain Hardy-type spaces

JO - Studia Mathematica

PY - 1994

VL - 111

IS - 2

SP - 195

EP - 206

AB - We consider a convolution operator Tf = p.v. Ω ⁎ f with $Ω(x) = K(x)e^{ih(x)}$, where K(x) is an (n,β) kernel near the origin and an (α,β), α ≥ n, kernel away from the origin; h(x) is a real-valued $C^∞$ function on $ℝ^n ∖ {0}$. We give a criterion for such an operator to be bounded from the space $H^{p}_{0}(ℝ^n)$ into itself.

LA - eng

KW - Hardy-type spaces; oscillating integrals

UR - http://eudml.org/doc/216128

ER -

## References

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- [7] Y. Han, Certain Hardy-type spaces, Ph.D. thesis, Washington University, St Louis, 1984.
- [8] Y. Han, A class of Hardy-type spaces, Chinese Quart. J. Math. 1 (2) (1986), 42-64.
- [9] W. B. Jurkat and G. Sampson, The complete solution to the $({L}^{p},{L}^{q})$ mapping problem for a class of oscillating kernels, Indiana Univ. Math. J. 30 (1981), 403-413. Zbl0507.47013
- [10] R. H. Latter, A characterization of ${H}^{p}\left({\mathbb{R}}^{n}\right)$ in terms of atoms, Studia Math. 62 (1978), 93-101. Zbl0398.42017
- [11] P. Sjölin, Convolution with oscillating kernels on ${H}^{p}$ spaces, J. London Math. Soc. 23 (1981), 442-454. Zbl0426.46034

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