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
كتاب
Lecture notes in mathematics Weighted Littlewood Paley Theory and Exponential Square Integrability
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