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 hln/m. 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 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 fo/the 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(w21/2→w21/2) 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-1/p() 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
