Abstract In this paper, we will study the Hardy and BMO spaces associated to generalized operator $$L_{\alpha }= (-\Delta )^{\alpha /2}+a|x|^{-\alpha }$$ L α = ( - Δ ) </mml:m...

Jachymski [ Proc. Amer. Math. Soc., 136 (2008), 1359-1373] gave modified version of a Banach fixed point theorem on a metric space endowed with a graph. In the present paper, (G, Φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. Also, Hardy-Rogers G-contraction have been introduced and some fixed point theorems have been proved. S...

Function spaces play a significant role in harmonic analysis and partial differential equations. The integral operators that form a bridge between function spaces and partial differential equations are the Calderón-Zygmund operators. It is well known that Calderón-Zygmund operators are bounded on the Lebesgue space L(R) for 1 < p < ∞. It is also known that the Calderón-Zygmund operators are not...

Hardy persons are hypothesized to be resistant to stress-induced illness, because of their adaptive cognitive style and a subsequently reduced level of physiological arousal. We assessed the cognitive and physiological responses of high and low hardy male undergraduates to a challenging task under high and low evaluative threat. As predicted, hardy subjects endorsed more positive self-statement...

In this paper, we consider composition operators on Hardy-Sobolev spaces in connections with BMO-quasiconformal mappings. Using the duality of Hardy and BMO-spaces, prove that mappings generate bounded from Hardy–Sobolev to Sobolev spaces.