Alberto Debernardi Pinos - Weighted norm inequalities for integral transforms with splitting kernels

cm:12756 - Communications in Mathematics, April 29, 2024, Volume 32 (2024), Issue 3 (Special issue: Portuguese Mathematics) - https://doi.org/10.46298/cm.12756
Weighted norm inequalities for integral transforms with splitting kernelsArticle

Authors: Alberto Debernardi Pinos

    We obtain necessary and sufficient conditions on weights for a wide class of integral transforms to be bounded between weighted LpLq spaces, with 1pq. The kernels K(x,y) of such transforms are only assumed to satisfy upper bounds given by products of two functions, one in each variable. The obtained results are applicable to a number of transforms, some of which are included here as particular examples. Some of the new results derived here are the characterization of weights for the boundedness of the Hα (or Struve) transform in the case α>12, or the characterization of power weights for which the Laplace transform is bounded in the limiting cases p=1 or q=.


    Volume: Volume 32 (2024), Issue 3 (Special issue: Portuguese Mathematics)
    Published on: April 29, 2024
    Accepted on: March 2, 2024
    Submitted on: December 30, 2023
    Keywords: Mathematics - Classical Analysis and ODEs,Mathematics - Functional Analysis,Primary: 42A38. Secondary: 26D15, 44A15

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