... S
n
(τ)todenotethesetofτ-avoiding
permutations in S
n
and, more generally, S
n
(T ) for the set of all permutations of length n
which avoid each pattern of the set T .
A central theme in the theory of ... permutation. Denote by D
1
the set of its diagram squares of rank at
most m − 3, and by D
2
the set of the remaining diagram squares.
Now de ne σ =Φ
m
(π) to be the permutatio...
... ∈S(R
n
),
then ϕ denotes the Fourier transform of ϕ, and ϕ
∨
denotes the inverse Fourier
transform of ϕ.
De nition 1. If 0 <q p<∞ and f ∈ L
q
Loc
(R
n
),wesayf ∈ M
p
q
(R
n
)
provided that, for ... Characterization of Morrey Type Besov and Triebel-Lizorkin Spaces 371
To make these space meaningful, the key point is to show that De nition 2
is independent of the choice of f...
... each function is de ned on V
5
⊂ J
5
Y .
References
1. I. M. Anderson, Aspect of the inverse problem to the calculus of variation, Arch.
Math. 24 (1988) 181–202.
2. I.M. Anderson and T. Duchamp, ... been considered by Anderson [1], Duchamp
[2], Dedecker [4], Tulczyvew [7], Takens [6] and Krupka [5]. The variational bi-
complex was mainly studied on the infinite jet prolongation J
∞
Y o...