A SYNOPSIS OF THE REVISED SYSTEM FOR THE CLASSIFICATION OF CHARACEAE

All charophytes,whether living or fossil,are placed in a single class,theCharophyceae.This is generally divided into the following three orders:theSycidiales,Trochiliscales,and Charales.All living genera are referred to the familyCharaceae.J.Groves‘(1935)and R.D.Wood‘s(1962)systems for the classification ofthe Characeae were quite generally followed until today.Groves and most phyco-logists think that the corticate forms(e.g.Chara)have been derived from the     

THE BOUNDEDNESS OF INTEGRAL OPERATORS OF A CLASS

Proposition If y(t), b(t) ∈ VDF ∩ VH(μ) ([1]), then||Ky||μ≤q||b||μ||y||μ,(1)where q is a constant and Ky=-b(t)/πi _L0 y(s) (ζ(t))ds.Proof. Let w(t) =1/πi _L_0 y(s)- y(t)/s-t ds and t_1-t_0=h. Suppose a path l = t't_0 U t_0t″, we obtainBy a complicated calculation, it can be got