Let σ=(σ1,σ2,⋯,σn)∈Sn−1 and dσ denote the normalized Lebesgue measure on Sn−1,n⩾2. For functions f1,f2,⋯,fn defined on R, consider the multilinear operator given by T(f1,f2,⋯,fn)(x)=∫Sn−1∏j=1nfj(x−σj)dσ,x∈R.In this paper...
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https://www.riss.kr/link?id=O112659715
2021년
-
0024-6093
1469-2120
SCI;SCIE;SCOPUS
학술저널
1045-1060 [※수록면이 p5 이하이면, Review, Columns, Editor's Note, Abstract 등일 경우가 있습니다.]
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
Let σ=(σ1,σ2,⋯,σn)∈Sn−1 and dσ denote the normalized Lebesgue measure on Sn−1,n⩾2. For functions f1,f2,⋯,fn defined on R, consider the multilinear operator given by T(f1,f2,⋯,fn)(x)=∫Sn−1∏j=1nfj(x−σj)dσ,x∈R.In this paper...
Let σ=(σ1,σ2,⋯,σn)∈Sn−1 and dσ denote the normalized Lebesgue measure on Sn−1,n⩾2. For functions f1,f2,⋯,fn defined on R, consider the multilinear operator given by
T(f1,f2,⋯,fn)(x)=∫Sn−1∏j=1nfj(x−σj)dσ,x∈R.In this paper, we obtain necessary and sufficient conditions on exponents p1,p2,⋯,pn and r for which the operator T is bounded from ∏j=1nLpj(R)→Lr(R), where 1⩽pj,r⩽∞,j=1,2,⋯,n. This generalizes the results obtained in (Bak and Shim, J. Funct. Anal. 157 (1998) 534–553; Oberlin, Trans. Amer. Math. Soc. 310 (1988) 821–835).
On Eagleson's theorem in the non‐stationary setup
Every bounded pseudo‐convex domain with Hölder boundary is hyperconvex