Embedding Theorems between Variable-Exponent Morrey Spaces

In this paper, we study various embedding theorems on variable-exponent Morrey spaces. In particular, we found a criterion characterizing embedding between variable-exponent Morrey spaces.

     

Commutators of fractional maximal operator on generalized Orlicz–Morrey spaces

In the present paper, we shall give necessary and sufficient conditions for the Spanne and Adams type boundedness of the commutators of fractional maximal operator on generalized Orlicz–Morrey spaces, respectively. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators.     

Some Characterizations of Lipschitz Spaces via Commutators on Generalized Orlicz–Morrey Spaces

In this paper, we give some new characterizations of the Lipschitz spaces via the boundedness of commutators associated with the fractional maximal operator, Riesz potential and Calderón–Zygmund operator on generalized Orlicz–Morrey spaces.     

The ground-state magnetic moments of odd-mass Hf isotopes

In this paper the Quasiparticle-Phonon Nuclear Model (QPNM), based on QRPA (Quasiparticle Random Phase Approximation) phonons, has been utilized to investigate spin polarization effects on the groundstate magnetic properties such as intrinsic magnetic moment (g _K ) and effective spin gyromagnetic factor (g _s ^eff. ) of odd-mass deformed ^165–179Hf isotopes with K > 1/2. Investigations of the spin polarization effects of the even core on the magnetic moments show that the spin gyromagnetic factors (g _s ) of the nucleons in the nucleus differ noticeably from the corresponding values for free nucleons and that the spin-spin interactions play an important role in the re-normalization of g _s factors of the odd-mass ^165–179Hf isotopes. In addition, some theoretical predictions are presented for the magnetic moments of ¹⁶⁵Hf, ¹⁶⁷Hf, and ¹⁶⁹Hf, whose ground state magnetic moments haven’t been experimentally determined yet.     

Low-lying magnetic dipole strength distribution in the γ-soft even-even 130-136Ba

In this study the scissors mode 1⁺ states are systematically investigated within the rotational invariant Quasiparticle Random Phase Approximation (QRPA) for ^130-136Ba isotopes. We consider the 1⁺ vibrations generated by the isovector spin-spin interactions and the isoscalar and isovector quadrupole-type separable forces restoring the broken symmetry by a deformed mean field according to A.A. Kuliev et al. (Int. J. Mod. Phys. E 9, 249 (2000)). It has been shown that the restoration of the broken rotational symmetry of the Hamiltonian essentially decreases the B(M1) value of the low-lying 1⁺ states and increases the collectivization of the scissors mode excitations in the spectroscopic energy region. The agreement between the calculated mean excitation energies as well as the summed B(M1) value of the scissors mode excitations and the available experimental data of ¹³⁴Ba and ¹³⁶Ba is rather good. A destructive interference between the orbit and spin part of the M1 strength has been found for barium isotopes near the shell closer. For all the nuclei under investigation, the low-lying M1 transitions have ΔK = 1 character as it is the case for the well-deformed nuclei.     

Gradient estimates for parabolic equations in generalized weighted Morrey spaces

We consider the Cauchy–Dirichlet problem for linear divergence form parabolic operators in bounded Reifenberg flat domain.The coefficients supposed to be only measurable in one of the space variables and small BMO with respect to the others.We obtain Calderón–Zygmund type estimate for the gradient of the solution in generalized weighted Morrey spaces with Muckenhoupt weight.     

Maximal Operator in Variable Exponent Generalized Morrey Spaces on Quasi-metric Measure Space

We consider generalized Morrey spaces \({\mathcal{L}^{p(\cdot),\varphi(\cdot)}( X )}\) on quasi-metric measure spaces \({X,d,\mu}\), in general unbounded, with variable exponent p(x) and a general function \({\varphi(x,r)}\) defining the Morrey-type norm. No linear structure of the underlying space X is assumed. The admission of unbounded X generates problems known in variable exponent analysis. We prove the boundedness results for maximal operator known earlier only for the case of bounded sets X. The conditions for the boundedness are given in terms of the so called supremal inequalities imposed on the function \({\varphi(x,r)}\), which are weaker than Zygmund-type integral inequalities often used for characterization of admissible functions \({\varphi}\). Our conditions do not suppose any assumption on monotonicity of \({\varphi(x,r)}\) in r.     

On the rearrangement estimates and the boundedness of the generalized fractional integrals associated with the Laplace-Bessel differential operator

We introduce the generalized fractional integrals (generalized B-fractional integrals) generated by the Δ _B Laplace-Bessel differential operator and give some results for them. We obtain O’Neil type inequalities for the B-convolutions and give pointwise rearrangement estimates of the generalized B-fractional integrals. Then we get the L _p,γ -boundedness of the generalized B-convolution operator, the generalized B-Riesz potential and the generalized fractional B-maximal function. Finally, we prove a sharp pointwise estimate of the nonincreasing rearrangement of the generalized fractional B-maximal function. V. S. Guliyev was partially supported by the grant of INTAS (Nr. 05-1000008-8157). Z. V. Safarov was partially supported by INTAS YS Post Doctoral Fellowship (Nr. 05-113-4671).     

O’Neil Inequality for Multilinear Convolutions and Some Applications

In this paper we prove the O’Neil inequality for the k-linear convolution f ⊗ g. By using the O’Neil inequality for rearrangements we obtain a pointwise rearrangement estimate of the k-linear convolution. As an application, we obtain necessary and sufficient conditions on the parameters for the boundedness of the k-sublinear fractional maximal operator M _{Ω, α} and k-linear fractional integral operator I _{Ω, α} with rough kernels from the spaces V.S. Guliyev partially supported by the grant of INTAS (project 05-1000008-8157).