Pictures for the “Counterexample to Sarason’s conjecture”.

I  I v  v v_{+} v_{−}  ^{J}

Figure 1: The original weight v (on the left) and the new one (on the right) for N = 3.

v_{3}  ṽ_{3} v_{2}  ṽ_{2} v_{1}  ṽ_{1} v_{0}  ṽ_{0} I  Ĩ I  Ĩ I  Ĩ I  Ĩ

Figure 2: The weights v_{0} – v_{3} (on the left) and the corresponding weights ṽ_{0} – ṽ_{3} (on the right) for N_{1} = N_{2} = 2, N_{3} = 3.

11  _{J_{1}}  _{J_{2}}

Figure 3: The function φ_{J,n} for n = 3 and the set E(J) consisting of two intervals J̃_{1} and J̃_{2}.