ineqrralit.y lO(t)l < clz - a.¡l "u@),u*(Q) ... t,râ¬1'\rf(u,)ur3(or). Considcr the following frr¡ictionai class: '11o,. (.l,.r,ut) * Jl",(tt,2.rr) -. \l e C", .... In ordr:r th.at thr: gr:n,eral,.
JOURNAL @Jnan
OF NATURAL
Bhawan,
GEOMETRY'
Lonclon.
22(2OO2)l-78
-22-r -r-r8. o963-26s4-2002 us$ 18.00. uKl
s.00.
Riemann Boundary Value Problem on a Regular Open Curve Dixan Peña Peña and Juan BorY ReYes
Abstract. In 1.hispa¡rer the Riernann Boundarl'Value Problen on a rectifiable open crrrve admitting the caseof the non-smooth curvc is studied. The solution of thc probler¡l is constructed explicitlv under some weak restricti 0
Pruof. To ut.k" $ "r*
suffir:iently srnall, srrch that for 1 € 1, (41) : 1 i¡,1¡i
I t Yll - o'l-''t'rl )'-ri '
o n t h e o t h e r h a n d s i n c c . g € H ' ( 1 , , t , u 1 ) * 7 1 " 2 ( ¡ t 2z, 2 ) , w e h a v e:
-.) l . s ( ¿s )ol ; l ( l r - o , l ) + { t ; ; ; ( l t - a z )o 0 is sufficientlv small and
f r l.
+ r, [¡r"¿1
if Lb e 7,, if Llr en.
3. It is ea*syto check that in [14, 7] the corresportding)r, ,\1, uk(G) arrduk(¿) verifr- the inequality reqrrestedin the Theorem4.1.
References A. A. B¿baev arrd \'. V. Salaer'. Bortntlar"¡1tto"l'ueproblt:m, and sing'ular r,nte'gral equal,'i,on.s on, recti,fiabll' u¡n.totLr.NIat. zarnel,ki, 31 (1982) 571-580.
l¿omoqeneous of soluti,onsof t,h,e. of l,h,r:n,um,br:r' E. A. Danilov, Th,cdr:pert.d.cnce D
