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Let K be a Calderón-Zygmund kernel and P a real polynomial defined on ℝⁿ with P(0) = 0. We prove that convolution with Kexp(i/P) is continuous on L²(ℝⁿ) with bounds depending only on K, n and the degree of P, but not on the coefficients of P.
Magali Folch-Gabayet, and James Wright. "An estimation for a family of oscillatory integrals." Studia Mathematica 154.1 (2003): 89-97. <http://eudml.org/doc/285177>.
@article{MagaliFolch2003, abstract = {Let K be a Calderón-Zygmund kernel and P a real polynomial defined on ℝⁿ with P(0) = 0. We prove that convolution with Kexp(i/P) is continuous on L²(ℝⁿ) with bounds depending only on K, n and the degree of P, but not on the coefficients of P.}, author = {Magali Folch-Gabayet, James Wright}, journal = {Studia Mathematica}, keywords = {principal value tempered distribution; oscillatory integral; Calderón-Zygmund kernel}, language = {eng}, number = {1}, pages = {89-97}, title = {An estimation for a family of oscillatory integrals}, url = {http://eudml.org/doc/285177}, volume = {154}, year = {2003}, }
TY - JOUR AU - Magali Folch-Gabayet AU - James Wright TI - An estimation for a family of oscillatory integrals JO - Studia Mathematica PY - 2003 VL - 154 IS - 1 SP - 89 EP - 97 AB - Let K be a Calderón-Zygmund kernel and P a real polynomial defined on ℝⁿ with P(0) = 0. We prove that convolution with Kexp(i/P) is continuous on L²(ℝⁿ) with bounds depending only on K, n and the degree of P, but not on the coefficients of P. LA - eng KW - principal value tempered distribution; oscillatory integral; Calderón-Zygmund kernel UR - http://eudml.org/doc/285177 ER -