content_image/304210.jpg content_image/304208.jpg content_image/304209.jpg
yields SG ( y/λ ) as 

and CLDR holds with this S and α = (1 , 1 , 2). 

<img src='content_image/304210.jpg'>

The next example demonstrates that the CLDR property may not hold for some G ( y ) even with q = p. 

Example 4.2. Consider 

with c ̸ = 0 . Then ¯ α = 2 . Consider an arbitrary 2 × 2 matrix S = ( s$_{ij}$ )$_{1}$$_{≤}$$_{i,j}$$_{≤}$$_{2}$ . 

<img src='content_image/304208.jpg'>

Three possibilities could arise for ¯ α = 2 if CLDR were to hold so that ¯ a = α$_{1}$ + α$_{2}$. 

First, α$_{1}$ = α$_{2}$ = 1 , then 

<img src='content_image/304209.jpg'>

does not exist, except if s$_{12}$ = s$_{22}$ = 0 , which is precluded for non-singular matrix S . 

