论文标题
广义加权洛伦兹空间之间的嵌入
Embeddings between generalized weighted Lorentz spaces
论文作者
论文摘要
我们给出了两个$Gγ$的功能空间之间连续嵌入的新表征。这样的空间由类型\ begin {方程*} \ | f \ | _ {gγ（r，q; w，δ）}的功能控制：= \ left（\ int_ {0}^{l} {l} {l} {l} \ left（\ frac1 \ right）^{\ frac {q} {r}} w（t）dt \ right）^\ frac1 {q}，\ end \ end {equation*}，其中$ f^*$是$ f $，$ f $，$ l \ in（0，\ infty] $，$，$，$，$ r，$ r，$ r，$ r，$ r f $ f $ f $ f $ f $ f $ f $ f $ f $ r， $（0，l）$和$δ（t）= \ int_ {0}^{t}δ（s）\，ds $ for $ ts $ for $ t \ in（0，l）$。 $gγ（R_2，Q_2; W_2，δ_2）$，意味着在四个正面参数和四个权重以适当的不平等能力上找到每个可允许的功能，我们将在早期的工作中享有$ n-decementy $ q限制主要是由于双重技术的使用而造成的，另一方面，我们在本文中避免了这一点。
We give a new characterization of a continuous embedding between two function spaces of type $GΓ$. Such spaces are governed by functionals of type \begin{equation*} \|f\|_{GΓ(r,q;w,δ)} := \left(\int_{0}^{L} \left( \frac1{Δ(t)} \int_0^t f^*(s)^r δ(s) ds \right)^{\frac{q}{r}} w(t) dt \right)^\frac1{q}, \end{equation*} in which $f^*$ is the nonincreasing rearrangement of $f$, $L\in(0,\infty]$, $r,q \in (0, \infty)$, $w, δ$ are weights on $(0,L)$ and $Δ(t)=\int_{0}^{t}δ(s)\,ds$ for $t\in(0,L)$. To characterize the embedding of such a space, say $GΓ(r_1,q_1;w_1,δ_1)$, into another, $GΓ(r_2,q_2;w_2,δ_2)$, means to find a balance condition on the four positive real parameters and the four weights in order that an appropriate inequality holds for every admissible function. We develop a new discretization technique which will enable us to get rid of restrictions on parameters imposed in earlier work such as the non-degeneracy conditions or certain relations between the $r$'s and $q$'s. Such restrictions were caused mainly by the use of duality techniques, which we avoid in this paper. On the other hand we consider here only the case when $q_1 \le q_2$, leaving the reverse case to future work.
