Hardy Spaces on the Euclidean Space pp 111-120 | Cite as

*S*-functions from *g*-functions

Chapter

## Abstract

(The statements of the results in this section are complicated. But, these results will not be used in later sections. You can skip this section.) In this section we will show that
For the definition of

*L*^{q}-norms of*S*ψδ*f*are essentially independent of the choice of ψ and*S*≥ 0 if ψ satisfies certain conditons. The point is the fact that this includes the case δ = 0. (The “*q*-function” in the title means Sψ0*f*) We write$$
\chi \left( x \right) = \chi _{B\left( {0,1} \right)} \left( x \right).
$$

(1)

*S*ψ,δ*m*recall Definition 3.6. In the notation*M*(*f** (φ)*t*)(*x*), the convolution * and the maximal operator*M*are taken with respect to the variable*x*∈**R**^{n}, with*t*∈ (0, +∞) fixed.## Keywords

Continuous Function Euclidean Space Number Theory Algebraic Geometry Hardy Space
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© Springer Japan 2001