# The Journal of Analysis

The Journal of Analysis > 2016 > 24 > 1 > 83-93

*f*analytic in the unit disk $${\mathbb D}$$ D and satisfying the normalization $$f(0)=0= f'(0)-1$$ f ( 0 ) = 0 = f ′ ( 0 ) - 1 . Let $$\mathcal {S}$$ S denote the subclass of $${\mathcal A}$$ A consisting of univalent functions in $${\mathbb D}$$ D . We consider the subclass $$\mathcal...

The Journal of Analysis > 2016 > 24 > 1 > 167-175

The Journal of Analysis > 2016 > 24 > 1 > 51-56

The Journal of Analysis > 2016 > 24 > 1 > 57-66

*G*of $${\mathbb R}^n$$ R n and their images $$G'=f(G)$$ G ′ = f ( G ) under quasiconformal mappings

*f*of $${\mathbb R}^n$$ R n . We compare the distance ratio metrics of

*G*and $$G'$$ G ′ ; as an application we show that $$\varphi $$ φ -uniform domains are preserved under quasiconformal mappings of $${\mathbb...

The Journal of Analysis > 2016 > 24 > 1 > 131-141

The Journal of Analysis > 2016 > 24 > 1 > 95-101

The Journal of Analysis > 2016 > 24 > 1 > 103-110

The Journal of Analysis > 2016 > 24 > 1 > 143-166

*p*Laplace equation, $$ - \infty< p < \infty , p \not = 1,2, $$ - ∞ < p < ∞ , p ≠ 1 , 2 , of degree four in $$ \mathbb {R}^{n}, n \ge 3, $$ R n , n ≥ 3 , and show there are no degree five real homogeneous polynomial solutions in $$ \mathbb {R}^{3}, $$ R 3 , when $$ - \infty< p <...

The Journal of Analysis > 2016 > 24 > 1 > 39-50

The Journal of Analysis > 2016 > 24 > 1 > 67-81

*f*is any uniformly quasiregular mapping with $$x_0$$ x 0 a topologically...

The Journal of Analysis > 2016 > 24 > 1 > 111-129

*j*-metric, $$\tilde{j}$$ j ~ -metric, the half-apollonian metric, and the hyperbolic metric. We also show that the density of the new metric is the same as the density of the quasihyperbolic metric.

The Journal of Analysis > 2016 > 24 > 1 > 1-38

The Journal of Analysis > 2016 > 24 > 2 > 229-250

The Journal of Analysis > 2016 > 24 > 2 > 177-181

The Journal of Analysis > 2016 > 24 > 2 > 183-208

*p*-modulus of a family of objects on a graph is a measure of the richness of such families. We develop the notion of minimal subfamilies using the method of Lagrangian duality for

*p*-modulus. We show that minimal subfamilies have at most |

*E*| elements and that these elements carry a weight related to their “importance” in relation to the corresponding

*p*-modulus problem. When $$p=2$$...

The Journal of Analysis > 2016 > 24 > 2 > 293-330

*harmonic measure distribution function*$$h:(0,\infty )\rightarrow [0,1]$$ h : ( 0 , ∞ ) → [ 0 , 1 ] of the pair $$(\Omega ,z_0)$$ ( Ω , z 0 ) maps each radius $$r > 0$$ r > 0 to the harmonic measure of the part of the boundary $$\partial...

The Journal of Analysis > 2016 > 24 > 2 > 331-345

The Journal of Analysis > 2016 > 24 > 2 > 209-228

The Journal of Analysis > 2016 > 24 > 2 > 277-291

The Journal of Analysis > 2016 > 24 > 2 > 251-276