Sharp maximal function estimates and H^p continuities of pseudo-differential operators

Key Points

• Weighted weak-type (1,1) estimates are established for pseudo-differential operators, enhancing existing understanding.
• Continuities in both (H^{p},H^{p}) and (H^{p},L^{p}) spaces showcase new relationships between operator properties and functional spaces.
• Pointwise estimates on Hardy spaces yield significant results for action of pseudo-differential operators within H"{o}rmander's classes.
• This work expands the toolbox for analysis by detailing continuity behavior of pseudo-differential operators in developed settings.