CONTENTS 1. Introduction and main results...............................................................5 2. Preliminaries.......................................................................................12 3. The sampling theorem and polar wavelet identity...............................25 4. Boundedness of almost diagonal matrices on $a^{αq}_{p}$...............27 5. Peetre's maximal inequality.................................................................31 6. Norm characterizations.......................................................................35 7. FHT multiplier and potential operators................................................39 8. Equivalence of $L^p$ and $A^{02}_p$, 1 < p < ∞...............................42 9. Conclusion..........................................................................................49 References.............................................................................................50
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