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Browsing Mathematics by Author "403c3eb6-c2a2-4754-b024-c4845c6eceb0"

Now showing items 1-9 of 9

CRITICAL HARDY INEQUALITIES

Ruzhansky, Michael; Suragan, Durvudkhan (SUOMALAINEN TIEDEAKATEMIA, 2019)

We prove a range of critical Hardy inequalities and uncertainty type principles on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. Moreover, we establish a new type of critical ...
Euler semigroup, Hardy–Sobolev and Gagliardo–Nirenberg type inequalities on homogeneous groups

Ruzhansky, Michael; Suragan, Durvudkhan; Yessirkegenov, Nurgissa (Springer, 2020-06-10)

In this paper we describe the Euler semigroup {e−tE∗E}t>0 on homogeneous Lie groups, which allows us to obtain various types of the Hardy–Sobolev and Gagliardo–Nirenberg type inequalities for the Euler operator E. Moreover, ...
GEOMETRIC HARDY AND HARDY-SOBOLEV INEQUALITIES ON HEISENBERG GROUPS

Ruzhansky, Michael; Sabitbek, Bolys; Suragan, Durvudkhan (SpringerOpen, 2020-07-04)

In this paper, we present geometric Hardy inequalities for the sub-Laplacian in half-spaces of stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space of the Heisenberg group ...
LINEAR DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS AND MITTAG-LEFFLER KERNELS

Fernandez, Arran; Restrepo, Joel E.; Suragan, Durvudkhan (Alexandria Engineering Journal, 2021-10-27)

Fractional differential equations with constant coefficients can be readily handled by a number of methods, but those with variable coefficients are much more challenging. Recently, a method has appeared in the literature ...
L-P-CAFFARELLI-KOHN-NIRENBERG TYPE INEQUALITIES ON HOMOGENEOUS GROUPS

Ozawa, Tohru; Ruzhansky, Michael; Suragan, Durvudkhan (OXFORD UNIV PRESS, 2019-03)

We prove L-P-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, which is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We also discuss some of their consequences. Already ...
(P,Q)-SUB-LAPLACIANS ON THE HEISENBERG GROUP

Abdikarim, Aidana; Suragan, Durvudkhan (Nazarbayev University School of Sciences and Humanities, 2020-08-01)

The main purpose of this capstone project is to do some analysis related to (p,q)-sub-Laplacians on the Heisenberg group. In the first part of the project, Green’s identities for (p,q)-sub-Laplacians are given on the ...
SUBELLIPTIC GEOMETRIC HARDY TYPE INEQUALITIES ON HALF‑SPACES AND CONVEX DOMAINS

Ruzhansky, Michael; Sabitbek, Bolys; Suragan, Durvudkhan (Duke University Press, 2020-04-02)

In this paper we present L2 and Lp versions of the geometric Hardy inequalities in half-spaces and convex domains on stratifed (Lie) groups. As a consequence, we obtain the geometric uncertainty principles. We give ...
Weighted L^{p}-Hardy and L^{p}-Rellich inequalities with boundary terms on stratified Lie groups

Ruzhansky, Michael; Sabitbek, Bolys; Suragan, Durvudkhan (Springer, 2018-06-29)

In this paper, generalised weighted Lp-Hardy, Lp-Caffarelli–Kohn–Nirenberg, and Lp-Rellich inequalities with boundary terms are obtained on stratified Lie groups. As consequences, most of the Hardy type inequalities and ...
Weighted L-p-Hardy and L-p-Rellich inequalities with boundary terms on stratified Lie groups

Ruzhansky, Michael; Suragan, Durvudkhan; Sabitbek, Bolys (SPRINGER-VERLAG ITALIA SRL, 2019-01)

In this paper, generalised weighted Lp-Hardy, Lp-Caffarelli-Kohn-Nirenberg, and Lp-Rellich inequalities with boundary terms are obtained on stratified Lie groups. As consequences, most of the Hardy type inequalities and ...