ok thanks again for your reply: this is what I worked out so far
#start code
xyplot(ped.avg ~ tv.avg | family, 
               data=mydata, 
               strip=strip.custom(bg='white'), col.line=1, main="title", 
               xlab = expression(paste('tv [ fg/', m^3, ' ]', sep = '')), 
                           ylab = expression(paste('ped [ fg/', m^3, ' ]', sep 
= '')),

               scales= list(x=list(relation="free", log=10), 
                            y=list(relation="free", log=10)
                                                        ),
                           as.table=TRUE,
                                                                                
        
               prepanel = function(x, y, ...) { 
        xlim=list(c(1, 3), c(0.2,2.8), c(1.8,3.8),c(1.8,3)) 
             ylim=list(c(1, 3), c(0.2,2.8), c(1.8,3.8),c(1.8,3)) 
        dx=list(c(1.4,1.8,2.2,2.6), c(0.6,1,1.4,1.8,2.2,2.6), 
c(2.2,2.6,3,3.4,3.8),
c(2.2,2.6,3))
        dy=list(c(1.4,1.8,2.2,2.6), c(0.6,1,1.4,1.8,2.2,2.6), 
c(2.2,2.6,3,3.4,3.8),
c(2.2,2.6,3))
                                  }, 
               panel = function(x, y,...) { 
                  panel.xyplot(x, y, cex=0.5,...) 
                  panel.abline(a = 0, b = 1, lty = 2, col ="gray") 
                  panel.text(x, y, lab = mydata$name, cex = 0.5, pos=3,
offset=1, srt=90)
                                                   }, 
               xscale.components = xscale.components.logpower, 
               yscale.components = yscale.components.logpower 
    ) 
#end code

but still something is not clear at all to me; 
I've been reading the help files but I must confesss that are quite obscure
to me; I would say there is a strange behaviour of this bit of code because
I can not properly get a fine control of each panel x and y axis

 prepanel = function(x, y, ...) { 
        xlim=list(c(1, 3), c(0.2,2.8), c(1.8,3.8),c(1.8,3)) 
             ylim=list(c(1, 3), c(0.2,2.8), c(1.8,3.8),c(1.8,3)) 
        dx=list(c(1.4,1.8,2.2,2.6), c(0.6,1,1.4,1.8,2.2,2.6), 
c(2.2,2.6,3,3.4,3.8),
c(2.2,2.6,3))
        dy=list(c(1.4,1.8,2.2,2.6), c(0.6,1,1.4,1.8,2.2,2.6), 
c(2.2,2.6,3,3.4,3.8),
c(2.2,2.6,3))
                                  }, 

I would like to have for each panel x and y axis equallly sped and with
equal limits; for some reasons I do not understand at all the aboe code did
not get the wanted result

any help for this?

thank you, this is indeed a good learning session to me

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