introduction
part i description and properties of multipliers
1 trace inequalities for functions in sobolev spaces.
1.1 trace inequalities for functions in wm1 and wm1
1.2 trace inequalities for functions in wmp and wmp，
p＞1
1.3 estimate for the lq-norm with respect to an arbitrary
measure
2 multipliers in pairs of sobolev spaces
2.1 introduction
2.2 characterization of the space m（wm1 → wl1）
2.3 characterization of the space m（wmp → wlp） for p＞1
2.4 the space m（wmp（rn+）→wlp（rn+））
2.5 the space m（wmp→w-kp）
2.6 the space m（wmp→wlp）
2.7 certain properties of multipliers
2.8 the space m（wmp→wlp）
2.9 multipliers in spaces of functions with bounded
variation.
3 multipliers in pairs of potential spaces
3.1 trace inequality for bessel and riesz potential
spaces
3.2 description of m（hmp→hlp）
.3.3 one-sided estimates for the norm in m（hmp→hlp）
3.4 upper estimates for the norm in m（hmp→hlp）by norms in besov
spaces
3.5 miseenaneous properties of multipliers in
m（hmp→hlp）
3.6 spectrum of multipliers in hlp and h-lp''
3.7 the space m（hmp→hlp）
3.8 positive homogeneous multipliers
4 the space m（bmp→blp） with p＞1
4.1 introduction
4.2 properties of besov spaces
4.3 proof of theorem 4.1.1
4.4 sufficient conditious for inclusion into m（wmp→wlp）with
noninteger m and l
4.5 conditions involving the space hlnm.
4.6 composition operator on m（wmp→wlp）
5 the space m（bm1→bl1）
5.1 trace inequality for functions in bl1（rn）
5.2 properties of functions in the space bk1（rn） ，
5.3 descriptions of-m（bm1→bl1） with integer l
5.4 description of the space-m（bm1→bl1） with noninteger
l
5.5 further results on multipliers in besov and other function
spaces
6 maximal algebras in spaces of multipliers
6.1 introduction
6.2 pointwise interpolation inequalities for
derivatives
6.3 maximal banach algebra in m（wmp→wlp）
6.4 maximal algebra in spaces of bessel potentials
6.5 imbeddings of maximal algebras
7 essential norm and compactness of multipliers
7.1 auxiliary assertions
7.2 two-sided estimates for the essential norm. the case
m＞l
7.3 two-sided estimates for the essential norm in the case m =
l
8.traces and extensions of multipliers
8.1 introduction
8.2 multipliers in pairs of weighted sobolev spaces in
rn+
8.3 characterization of m（wpt，→wps，）
8.4 auxiliary estimates for an extension operator
8.5 trace theorem fothe space m（wpt，→wps，
8.6 traces of multipliers on the smooth boundary of a
domain.
8.7 mwlp（rn） as the space of traces of multipliers in the
weighted sobolev space wp，k（r+n+1）
8.8 traces of functions in mwpl（rn+m） on rn
8.9 multipliers in the space of bessel potentials as traces of
multipliers
9 sobolev multipliers in a domain， multiplier mappings and
manifolds
9.1 multipliers in a special lipschitz domain
9.2 extension of multipliers to the complement of a special
lipschitz domain
9.3 multipliers in a bounded domain
9.4 change of variables in norms of sobolev spaces
9.5 implicit function theorems
9.6 space
part ii applications of multipliers to differential and integral
operators
10 differential operators in pairs of sobolev spaces
10.1 the norm of a differential operator： wph→wph-k
10.2 essential norm of a differential operator
10.3 fredholm property of the schr6dinger operator
10.4 domination of differential operators in rn
11 schrsdinger operator and m（w21→w2-1）
11.1 introduction
11.2 characterization of m（w21→w2-1） and the schrodinger
operator on w12
11.3 a compactness criterion
11.4 characterization of m（w21→w2-1）
11.5 characterization of the space m（w21（）→w2-1（））
11.6 second-order differential operators acting from w21 to
w21
12 relativistic schrsdinger operator and
m（w212→w212）
12.1 auxiliary assertions
12.2 corollaries of the form boundedness criterion and related
results
13 multipliers as solutions to elliptic equations
13.1 the dirichlet problem for the linear second-order-elliptic
equation in the space of multipliers
13.2 bounded solutions of linear eniptic equations as
multipliers
13.3 solvability of quasilinear elliptic equations in spaces of
multipliers
13.4 coercive estimates for solutions of elliptic equations in
spaces of multipliers
13.5 smoothness of solutions to higher order elliptic semilinear
systems
14 regularity of the boundary in lv-theory of elliptic boundary
value problems
14.1 description of results
14.2 change of variables in differential operators
14.3 fredholm property of the elliptic b?undary value
problem
14.4 auxiliary assertions
14.5 solvability of the dirichlet problem in wlp（）
14.6 necessity of assumptions on the domain
14.7 local characterization of mpl-1p（）
15 multipliers in the classical layer potential theory for
lipschitz domains
15.1 introduction
15.2 solvability of boundary value problems in weighted sobolev
spaces
15.3 continuity properties of boundary integral
operators
15.4 proof of theorems 15.1.1 and 15.1.2
15.5 properties of surfaces in the class mpl（）
15.6 sharpness of conditions imposed on
15.7 extension to boundary integral equations of
elasticity
16 applications of multipliers to the theory of integral
operators
16.1 convolution operator in weighted l2-spaces
16.2 calculus of singular integral operators with symbols in
spaces of multipliers
16.3 continuity in sobolev spaces of singular integral operators
with symbols depending on x
references
list of symbols
author and subject index
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