2008م - 1444هـ
نبذه عن الكتاب:



Littlewood-Paley theory can be thought of as a profound generalization of the

Pythagorean theorem. If x ∈ Rd—say, x = (x1, x2, ... , xd)—then we define

x’s norm, x, to be (
d

1 x2

n)1/2. This norm has the good property that, if

y = (y1, y2, ... , yd) is any other vector in Rd, and |yn|≤|xn| for each n, then

y≤x. In other words, the size of x, as measured by the norm function,

is determined entirely by the sizes of x’s components. This remains true if

we let the dimension d increase to infinity, and define the norm of a vector

(actually, an infinite sequence) x = (x1, x2, ...) to be x ≡ (


∞

1 x2

n)1/2.

In analysis it is often convenient (and indispensable) to decompose functions f into infinite series