L p(·)−L q(·) Estimates for Some Convolution Operators with Singular Finite Measures

URCIUOLO, M.; VALLEJOS, L.

ANALYSIS MATHEMATICA

AKADEMIAI KIADO RT

Año: 2022 vol. 48 p. 849 - 860

0133-3852

Let μ be the surface measure on ℝn+1 supported on the graph of φ(y1,…,yn)=|y1|β1+⋯+|yn|βn, (y1, …, yn) ∈ [−1, 1]n and let Tμbe the convolution operator given by Tµf(x)=µ*f(x)=∫Rn+1f(x-y)dµ(y). We obtain necessary conditions on the exponent functions p(·) and q(·) for the boundedness of Tμ from Lp(·) (Rn+1) into Lq(·) (Rn+1) and we also prove sufficient conditions for certain pairs (p(·), q(·)).