Properties of integrals which have the type of derivatives of volume potentials for one ultraparabolic arbitrary order equation

V. S. Dron', S. D. Ivasyshen, I. P. Medyns'kyi

Abstract


Properties of integrals which have the type of derivatives of volume potentials for one Kolmogorov type ultraparabolic arbitrary order equation}{In weighted H\"older spaces it is studied the smoothness of integrals, which have the structure and properties of derivatives ofvolume potentials which generated by fundamental solutions of the Cauchy problem for one ultraparabolic arbitrary order equation of the Kolmogorov type.The coefficients in this equation depend only on the time variable.Special distances and norms are used for constructing of the weighted H\"older spaces.
The results of the paper can be used for establishing of the correct solvability of  the Cauchy problem and estimates of solutionsof the given non-homogeneous equation in corresponding weighted H\"older spaces.


Keywords


ultraparabolic Kolmogorov type arbitrary order equation, an integral which have the type of derivatives of the volume potential, weight H\"older norm, H\"older space of increasing functions

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