Weighted Lp-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces

Kazumasa Fujiwara; Tohru Ozawa

doi:10.2969/jmsj/06810169

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Weighted L^p-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces

Kazumasa Fujiwara, Tohru Ozawa

著者情報

キーワード: pointwise multiplication, Sobolev spaces

ジャーナルフリー

2016 年 68 巻 1 号 p. 169-191

DOI https://doi.org/10.2969/jmsj/06810169

詳細

抄録

We study the boundedness of integral operators of convolution type in the Lebesgue spaces with weights. As a byproduct, we give a simple proof of the fact that the standard Sobolev space H^s(ℝⁿ) forms an algebra for s > n/2. Moreover, an optimality criterion is presented in the framework of weighted L^p-boundedness.