Premium
Some Sharp Bounds for the Cone Multiplier of Negative Order in R 3
Author(s) -
Lee Sanghyuk
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002005
Subject(s) - mathematics , multiplier (economics) , cone (formal languages) , combinatorics , operator (biology) , mathematics subject classification , order (exchange) , algorithm , chemistry , finance , economics , biochemistry , repressor , gene , transcription factor , macroeconomics
This paper considers the cone multiplier operator which is defined byS μ f ^ ( ξ , τ ) = m μ ( ξ , τ ) f ^ ( ξ , τ ) , ( ξ , τ ) ∈ R 2 × Rwherem μ ( ξ , τ ) = φ ( τ )( 1 − | ξ | 2 / τ 2 ) + μ / Γ ( μ + 1 )and φ ∈ C 0 ∞ ( 1 , 2 ) . For −3/2 < μ < −3/14, sharp L p − L q estimates and endpoint estimates for S μ are obtained. 2000 Mathematics Subject Classification 42B15 (primary).