sobolp.dim<-function(dims,p,bets)
{
r<-0
g<-0

dlen<-length(dims)
over<-matrix(0,dlen,1)
lowe<-matrix(0,dlen,1)

for (i in 1:dlen){

d<-dims[i]
betta<-bets[i]

q<-p*(betta-d/p+d/2)
musd<-2*pi^(d/2)/gamma(d/2)

# upper bound

if (p>1){

pote1<-((p-1)/p)*(g+r+d/2)/(betta+g)
pote2<-(1/2)*(betta-r-d/2)/(betta+g)
kup<-musd
ku2<-musd
a1<-(p*(q-r)/(p-1)-q-d)/(q+2*g)
a2<-(q+p*(2*g+r)/(p-1)+d)/(q+2*g)
b1<-(2*(q+g-r)-d)/(q+2*g)  
b2<-(2*(g+r)+d)/(q+2*g)
I1<-(2*pi)^(d*(1-p/(p-1)))*kup*beta(a1,a2)/(q+2*g)
I2<-(2*pi)^(-d)*ku2*beta(b1,b2)/(q+2*g)
vakio<-((g+r+d/2)/(betta-r-d/2))^((betta-r-d/2)/(betta+g))*(betta+g)/(g+r+d/2)
yla<-I1^pote1*I2^pote2*vakio

over[i]<-yla
}

# lower bound

if (p>1){

pote3<-(-1/p)*(g+r+d/2)/(betta+g)
pote4<-(-1/2)*(betta-r-d/2)/(betta+g)
kl3<-musd
kl4<-musd
kl5<-musd
c1<-(p*(q+g)/(p-1)-q-p*(g+r)-d)/(q+2*g)
c2<-(q+p*g/(p-1)+p*(g+r)+d)/(q+2*g)
d1<-(2*(q+g)/(p-1)-2*r-d)/(q+2*g)
d2<-(2*g/(p-1)+2*r+d)/(q+2*g)
e1<-((q+g*(2-p))/(p-1)-2*r-d)/(q+2*g)
e2<-(p*g/(p-1)+2*r+d)/(q+2*g)
I3<-(2*pi)^(d*(1-p/(p-1)))*kl3*beta(c1,c2)/(q+2*g)
I4<-(2*pi)^(d*(1-2/(p-1)))*kl4*beta(d1,d2)/(q+2*g)
I5<-(2*pi)^(-d/(p-1))*     kl5*beta(e1,e2)/(q+2*g)
ala<-I3^pote3*I4^pote4*I5

lowe[i]<-ala
}

# L1 constant

if (p==1){
   kappa<-(betta-r-d/2)/(betta+g)
   i1<-(2*pi)^(-d)
   i2<-2*musd*(q-r)^2/((2*pi)^d*(2*g+2*r+d)*(q+2*g+r+d)*(2*q+2*g+d))
   vakil1<-((g+r+d/2)/(betta-r-d/2))^kappa*(betta+g)/(g+r+d/2)
   lic<-(i2^(1/2))^kappa*i1^(1-kappa)*vakil1

   lowe[i]<-lic
   over[i]<-lic
}

}

return(list(lowe=lowe,over=over))

}