We introduce a class of generalized Orlicz-type Auscher-Mourgoglou slice space,which is a special case of the Wiener amalgam.We prove versions of the Rubio de Francia extrapolation theorem in this space.As a consequen...We introduce a class of generalized Orlicz-type Auscher-Mourgoglou slice space,which is a special case of the Wiener amalgam.We prove versions of the Rubio de Francia extrapolation theorem in this space.As a consequence,we obtain the boundedness results for several classical operators,such as the Calderón-Zygmund operator,the Marcinkiewicz integrals,the Bochner-Riesz means and the Riesz potential,as well as variational inequalities for differential operators and singular integrals.As an application,we obtain global regularity estimates for solutions of non-divergence elliptic equations on generalized Orlicz-type slice spaces if the coefficient matrix is symmetric,uniformly elliptic and has a small(δ,R)-BMO norm for some positive numbers δ and R.展开更多
Let φ be a generalized Orlicz function satisfying(A0),(A1),(A2),(aInc)and(aDec). We prove that the mapping f■f^#:=supB|1/B|∫B|f(x)-fp|dx is continuous on L^φ(·)(R^n) by extrapolation. Based on this result we ...Let φ be a generalized Orlicz function satisfying(A0),(A1),(A2),(aInc)and(aDec). We prove that the mapping f■f^#:=supB|1/B|∫B|f(x)-fp|dx is continuous on L^φ(·)(R^n) by extrapolation. Based on this result we generalize Korn's inequality to the setting of generalized Orlicz spaces, i.e., ‖■f‖Lφ(·)(Ω)■‖Df‖Lφ(·)(Ω). Using the Calderón–Zygmund theory on generalized Orlicz spaces, we obtain that the divergence equation divu = f has a solution u ∈(W^1φ(·)(Ω)0)^n such that ‖■f‖Lφ(·)(Ω)■‖f‖Lφ(Ω).展开更多
This paper is concerned with the existence theory of a semilinear elliptic system. In particular, we will prove that the system has a nontrivial positive solution in some appropriate solution spaces.
基金supported by the National Natural Science Foundation of China(11726622)the Natural Science Foundation Projection of Chongqing,China(cstc2021jcyj-msxmX0705).
文摘We introduce a class of generalized Orlicz-type Auscher-Mourgoglou slice space,which is a special case of the Wiener amalgam.We prove versions of the Rubio de Francia extrapolation theorem in this space.As a consequence,we obtain the boundedness results for several classical operators,such as the Calderón-Zygmund operator,the Marcinkiewicz integrals,the Bochner-Riesz means and the Riesz potential,as well as variational inequalities for differential operators and singular integrals.As an application,we obtain global regularity estimates for solutions of non-divergence elliptic equations on generalized Orlicz-type slice spaces if the coefficient matrix is symmetric,uniformly elliptic and has a small(δ,R)-BMO norm for some positive numbers δ and R.
基金Supported by the National Natural Science Foundation of China (Grant No.11726622)Scientific Research Fund of Young Teachers in Longqiao College (Grant No. LQKJ2020-01)。
文摘Let φ be a generalized Orlicz function satisfying(A0),(A1),(A2),(aInc)and(aDec). We prove that the mapping f■f^#:=supB|1/B|∫B|f(x)-fp|dx is continuous on L^φ(·)(R^n) by extrapolation. Based on this result we generalize Korn's inequality to the setting of generalized Orlicz spaces, i.e., ‖■f‖Lφ(·)(Ω)■‖Df‖Lφ(·)(Ω). Using the Calderón–Zygmund theory on generalized Orlicz spaces, we obtain that the divergence equation divu = f has a solution u ∈(W^1φ(·)(Ω)0)^n such that ‖■f‖Lφ(·)(Ω)■‖f‖Lφ(Ω).
文摘This paper is concerned with the existence theory of a semilinear elliptic system. In particular, we will prove that the system has a nontrivial positive solution in some appropriate solution spaces.
